Modeling the effects of hydrodynamics, suspended sediments, and water quality on light attenuation in Indian River Lagoon, Florida

UFL/COEL-2001/0 I/

MODELING THE EFFECTS OF HYDRODYNAMICS, SUSPENDED
SEDIMENTS, AND WATER QUALITY ON LIGHT
ATTENTUATION IN INDIAN RIVER LAGOON, FLORIDA

by

DAVID JOSEPH CHRISTIAN

THESIS

2001

Coastal & Oceanographic Engineering Program
Department of Civil & Coastal Engineering
433 Weil Hall *P.O. Box 116590 Gainesville, Florida 32611-6590

UNIVERSITY OF
FLORIDA

UFL/COEL-2001/017

MODELING THE EFFECTS OF HYDRODYNAMICS, SUSPENDED
SEDIMENTS, AND WATER QUALITY ON LIGHT
ATTENTUATION IN INDIAN RIVER LAGOON, FLORIDA

by

DAVID JOSEPH CHRISTIAN

THESIS

2001

MODELING THE EFFECTS OF HYDRODYNAMICS,
SUSPENDED SEDIMENTS, AND WATER QUALITY ON LIGHT ATTENUATION
IN INDIAN RIVER LAGOON, FLORIDA

By

DAVID JOSEPH CHRISTIAN

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2001

Copyright 2001

by

David Joseph Christian

I dedicate this thesis to my family, whose love and support have helped me get to where I
am.

ACKNOWLEDGMENTS

I would like to thank the chairman of my committee, Dr. Peter Sheng, for his support

and guidance throughout my master's study. I would also like to thank the other members

of my committee, Dr. Robert Dean and Dr. Edward Phlips, for their help and insight.

The St. Johns River Water Management District funded the IRLPLR (Indian River

Lagoon Pollutant Load Reduction) model development project, which provided me the

opportunity to study light attenuation processes in the IRL. I need to extend a special thank

you to Justin Davis, Haifang Du, Detong Sun, Chenxia Qiu, and all of Dr. Sheng's other

students for their help and friendship. I am also indebted to Adam Kornick who started the

light attenuation work. I also cannot thank Dr. Chuck Gallegos enough for providing

information on his model and answering my long list of questions. A big thank you goes out

to the crew at the coastal lab, Sidney, Vik, Vernon, Chuck, and J. J., for helping with field

and lab work and being understanding when we brought something back from the field

broken. I would also like to thank Terry Johnson for helping with my diving.

Finally, I need to thank Kim Christmas for her friendship, support, and love. I could

not have made it without her.

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS ............................................... iv

LIST OFTABLES ..................................................... ix

LISTOFFIGURES ............................................... xv

ABSTRACT ......................................................... xxi

1 INTRODUCTION AND BACKGROUND .............................. 1

1.1 Introduction and Background .......................................... 1
1.2 Light Definitions .................................................... 6
1.3 Seagrass and PAR Relationships ....................................... 13
1.4 Previous Light Attenuation M odels .................................... 15
1.5 This Study ..................... ............................... 18

2 DATA SETS ...................................................... 20

2.1 Introduction .................................................... ... 20
2.2 Sampling Procedures ............................................. .. 20
2.2.1 SERC Data Set ............................................. 20
2.2.2 UF Data Set ............................................... 22
2.2.3 WQMN Data ............................................ .. 25
2.2.4 HBOI Data ................................................. 25
2.2.5 Phlips Data ................................................. 27
2.3 Data Set Statistics .................................................. 28
2.3.1 SERC Data Set ..................................... ....... 28
2.3.2 UF Data Set ............................................ 29
2.3.3 WQMNDataSet ........................................... 30
2.3.4 HBOI Data Set ........................................... 31
2.3.5 Phlips Data Set .................................... ..........33
2.3.6 All Data Sets Comparison ..................................... 33

v

2.4 The Relative Importance of Various Factors for Light Attenuation ............. 34
2.4.1 Equations Used to Calculate Kd(PAR) Attributable to Each Variable .... 35
2.4.2 Data Set Analysis ........................................... 36
2.4.3 Percentage of Each Measured K/PAR) Due to Each Variable ......... 37
2.4.4 Analysis by Section .........................................42
2.4.5 Analysis by Season ......................................... 43
2.5 Data Differences ................................................... 45
2.5.1 UFData .................................................. 46
2.5.2 WQMN Data .............................................. 47
2.5.3 HBOIData ................................................ 51
2.5.4 Attempt to Make TSS Data Uniform ............................55
2.6 Data Sets Statistics With Converted TSS Values ........................... 57
2.6.1 Converted TSS Data Sets ..................................... 57
2.6.2 Season's Statistics ................ ......................... 58
2.6.3 Section's Statistics .......................................... 59

3 REGRESSION MODELS ............................................ 64

3.1 Introduction ...................................... ........... ... . 64
3.2 Regression Model Statistics ................ ......................... 66
3.3 Regression Models for Various Data Sets .............................. 69
3.3.1 Best One-Variable Linear Regression Model for Each Data Set ........ 69
3.3.2 Best Two-Variable Linear Regression Model for Each Data Set ....... 71
3.3.3 Best Three-Variable Linear Regression Model for Each Data Set ...... 72
3.3.4 Best Three Variable Factorial Regression Model for Each Data Set ..... 76
3.4 Best Regression Models for Seasonal Data Sets ............................ 77
3.4.1 Best One-Variable Linear Regression Model for Each Season ......... 77
3.4.2 Best Two-Variable Linear Regression Model for Each Season ......... 80
3.4.3 Best Three-Variable Linear Regression Model for Each Season ........ 81
3.4.4 Best Three-Variable Factorial Regression Model for Each Season ...... 82
3.5 Best Regression Models for Each Section of the IRL ........................ 83
3.5.1 Best One-Variable Linear Regression Models for Each Section ........ 83
3.5.2 Best Two-Variable Linear Regression Model for Each Section ........ 85
3.5.3 Best Three-Variable Linear Regression Model for Each Section ....... 87
3.5.4 Best Three-Variable Factorial Regression Model for Each Section ..... 88
3.6 Summary of Regression Models ........................................ 89

4 NUMERICAL MODEL ........................................... 91

4.1 Introduction ........................... .......................... 91
4.2 Kirk's W ork ................................ ..................... 91
4.3 Gallegos's W ork .... ............................. ................. 93
4.3.1 Absorption by Water ...................................... 94

4.3.2
4.3.3
4.3.4
4.3.5
4.3.6
4.3.7
4.4 PARPS

Absorption by Yellow Substance ...........
Absorption by Phytoplankton .............
Absorption by Detritus ...................
Scattering by Particles ...................
Use of Absorption and Scattering Coefficients
Gallegos's Calibration for Use in the IRL ....
M odel ..............................

..... 94
..... 96
.....96
.....97
..... 98
.... 100
.... 102

5 NUMERICAL MODEL OF LIGHT ATTENUATION ......

5.1 Introduction ...................................................... 105
5.2 Debugging ........................................................106
5.3 Individual Data Set Runs ................ .......................... 106
5.3.1 Full Collected Data Sets ..................................... 107
5.3.2 Data Sets by Season ................ ....................... 116
5.3.3 Data Sets of Sections ........................................ 117
5.4 Alternate Model Coefficients ................ ....................... 120
5.4.1 Each Season's Coefficients .................................. 128
5.4.2 Each Section's Coefficients ............... ................. .132
5.4.3 Comparison of Monte Carlo Coefficients to Experimental Coefficients 140

5.5 Alternate TSS-Turbidity Relationships

.. . . . . . . . . . . . . .. . 14 0

6 INTEGRATED MODEL RESULTS ................................

6.1 Introduction ...................................................
6.2 Model Architecture ..............................................
6.2.1 Allparpsworkch3d.f ....................................
6.2.2 Light Calculations .......................................
6.3 Segment Analysis ......................... .......................
6.3.1 Com prison to Data ......................................
6.3.2 Time Series Analysis .....................................

7 CONCLUSIONS ................ ......

.......................... 174

7.1 D ata Sets ....................
7.2 Individual Light Attenuation Models
7.3 Integrated Light Attenuation Model
7.4 Future W ork ..................

APPENDIX A ....................

APPENDIX B .............................. ........................ 187

..145
..145
..146
..147
..156
..157
..158

.... 174
.... 175
.... 177
.... 178

111 1111

111 111

A PPEN D IX C ........................................................ 190

LIST OFREFERENCES ................................................ 203

BIOGRAPHICAL SKETCH ............................................ 207

LIST OF TABLES

Table Page

2.1. Sample sites used in the SERC study. ................................ 21

2.2. SERC water quality variables used in the light attenuation model ........... 22

2.3. UF synoptic sampling trips were carried out on these dates ................ 23

2.4. UF water quality variables used in the light attenuation model. ............. 23

2.5. Sample sites used during UF synoptic sampling trips. ..................... 24

2.6. Additional sampling sites used during UF sampling trips 1-6 ............... 25

2.7. Sites sampled during WQMN sampling trips ........................... 26

2.8. HBOI water quality variables used in the light attenuation model ........... 27

2.9. Sample sites used during the HBOI study............................... 27

2.10. Data set statistics for the data collected during the SERC study. ............ 28

2.11. Statistics for the data collected during UF synoptic sampling
trips 1-6......................................................... 29

2.12. Statistics for the data collected during UF synoptic sampling trips 7-12 without
transformed TSS. ............................................... 30

2.13. Data set statistics for data collected by WQMN from March 1996
through 1998. .................................................. 31

2.14. Data set statistics for data collected by WQMN between March and May 1999
without transformed TSS. .................................... ..... 31

2.15. Data set statistics for HBOI data collected during HBOI's first sampling year
without transformed TSS. ..................................... 32

2.16. Data set statistics for HBOI data collected during HBOI's second sampling
year without transformed TSS. ..................................... 32

2.17. Data set statistics for data collected by Phlips during their October 1999
sampling trip in which TSS data were collected ........................ 33

2.18. Mean values of variables of interest from each of the data sets used in this
study without transformed TSS data .................................. 34

2.19. Percent of Kd(PAR) due to each attenuator in this study. .................. 37

2.20. Percentage of KdPAR) due to color, chlorophyll a, and tripton for each
data set for KdPAR) values above and below 1.00 m1 ..................... 40

2.21. Percentage of KdPAR) due to color, chlorophyll a, and tripton for each data
set for KdPAR) values above and below the mean KdPAR) value for each
data set. ................... ................................. ... 41

2.22. Percent of KdPAR) due to color, chlorophyll a, and tripton for each
section of the IRL. .................................... ............ 43

2.23. Percent of KdPAR) due to color, chlorophyll a, and tripton for
each season. ..................................................... 44

2.24. Turbidity calculations using HBOI years 1 and 2 average TSS values ........ 54

2.25. KdPAR) calculations using HBOI years 1 and 2 average TSS values. ........ 54

2.26. Results from TSS split sample analysis. ............................. .56

2.27. Transformed TSS statistics using WQMN 1994-1998 and WQMN 1999
turbidity-TSS relationships. .......... .............................. 58

2.28. TSS statistics for data transformed using WQMN 1994-1998 and WQMN
1999 turbidity-TSS relationships. .................................... 59

2.29. Statistics for January March with transformed TSS values. ............... 60

2.30. Statistics for April June with transformed TSS. ......................... 61

2.31. Statistics for July September with transformed TSS. .................... 61

2.32. Statistics for October December with transformed TSS.................... 61

2.33. Statistics for the South Section of the IRL with transformed TSS ........... 62

2.34. Statistics for the Middle Section of the IRL with transformed TSS .......... 62

2.35. Statistics for the North Section of the IRL with transformed TSS ............ 62

2.36. Statistics for the Banana River with transformed TSS .................... 63

2.37. Statistics for the Mosquito Lagoon with transformed TSS ................. 63

3.1. Best one-variable regression model for each data set ..................... 70

3.2. F values and p values for the best one-variable regression models. ......... 71

3.3. Best two-variable model for each data set. .......................... . 72

3.4. F values andp values for the best two-variable regression models. .......... 73

3.5. Best three-variable regression model for each data set ..................... 74

3.6. R2 values for the best three-variable model for each data set and the
improvement in R2 over the two- variable model. ........................ 74

3.7. F values and p values for each variable in three-variable regression models.
.................................................... .......... .75

3.8. R2 values for the best three-variable factorial model for each data set
and the R2 improvement over the best three-variable regression model for each
data set. ...................................................... .76

3.9. Best three-variable factorial model for each data set. ...................... 78

3.10. Best one-variable model for each season. .............................. 79

3.11. F values and p values for each season's best one-variable model. ........... 80

3.12. Best two-variable model for each season. .............................. 80

3.13. F values andp values for each season's best two variable model. ........... 81

3.14. Best three variable model for each season. .................. ........ . 81

3.15. R2 for the best three variable regression model for each season and the R2
improvement over the best two variable models. ........................ 82

3.16. F values and p values for each season's best three variable regression model. .. 82

3.17. R2 for the three variable factorial model for each season and the R2
improvement over the three variable regression models.................... 83

3.18. Best three variable factorial model for each season ....................... 84

3.19. Best one-variable regression model for each section. ...................... 85

3.20. F values and p values for the best one-variable regression model for
each section. .................................................... 85

3.21. Best two-variable regression model for each section. ...................... 86

3.22. F values and p values for the best two-variable model for each section........ 86

3.23. Best three-variable regression model for each section. ..................... 87

3.24. R2 for the best three-variable regression model for each section and the R2
improvement over the best two-variable model for each section ............ 87

3.25. F values and p values for the best three-variable regression model for each
section. .............................................. ........... 88

3.26. R2 for each section's best three-variable factorial model and the R2
improvement over the best three-variable regression model for each section. .. 89

3.27. Best three-variable factorial model for each section ...................... 90

4.1. Absorption by water per wavelength. ................................ 95

4.2. Absorption by chlorophyll per wavelength. .................. ...... .. 97

4.3. Spectral incident PAR values. ............................... ....... 100

4.4. Gallegos's model coefficients for the Marker 198 sample site ............. 101

4.5. Gallegos's model coefficients for the Ft. Pierce Inlet sample site. .......... 101

4.6. Kornick's model coefficients for the entire IRL. ................... ..... 104

5.1. RMS errors (m-1) of Kd(PAR) for numerical model runs using Marker 198
coefficients and Ft. Pierce coefficients .............................. 107

5.2. Mean Standard Deviation (m'1) from model results and data for each
data set. ....................................................... 108

5.3. RMS errors (m-') for numerical model runs for each season using Marker 198
coefficients and Ft. Pierce coefficients. .............................. 116

5.4. Mean Standard Deviation (mi') from model results and data for
each season ................................................... 117

5.5. RMS errors (m-') of Kd(PAR) for numerical model runs for each section
using Marker 198 coefficients and Ft. Pierce coefficients. ................ 120

5.6. Mean and Standard Deviation (m-1) of Kd(PAR) from model results and data
for each section ................... ........................ .... 121

5.7. Coefficient ranges for use in Monte Carlo model ....................... 125

5.8. Results for SERC One Thousand Run Monte Carlo Tests With Sy = 0.016. ... 126

5.9. Comparison of RMS errors for each data set using Ft. Pierce coefficients and
SERC monte carlo coefficients with Sy = 0.0160 ........................ 127

5.10. Comparison of means standard deviations (mn') for KdPAR) from data,
model results with Ft. Pierce coefficients, and SERC monte carlo coefficients
with sy = 0.0160 ................... ....................... ....... 128

5.11. Coefficients for each of the seasons found by Monte Carlo method. ........ 133

5.12. Comparison of RMS errors of Kd(PAR) for model runs for each season
using the coefficients found by monte carlo method for each season,
coefficients found by monte carlo method for the SERC set, and the
Ft. Pierce coefficients (m-1). .................. ............. ....... 133

5.13. Comparison of mean and standard deviation of modeled KdPAR) values for
each season using the coefficient set determined for the SERC data set with
the monte carlo method, the Ft. Pierce coefficient set, and data (m-n) ........ 133

5.14. Coefficients found for each section by monte carlo method................ 137

5.15. Comparison of RMS errors for model runs for each section using the
coefficients found by monte carlo method for each section, coefficients
found by monte carlo method for the SERC set, and the Ft. Pierce
coefficients (m-'). .............................................. 137

5.16. Comparison of mean and standard deviation of modeled KdPAR) values
for each section using the coefficient set determined for the SERC data set
with the monte carlo method, the Ft. Pierce coefficient set, and data (m-'). ... 137

5.17. Comparison of RMS Error Values for the Northern IRL Data of Each Data Set
using Gallegos's Turbidity TSS Equation and the Turbidity TSS Equation
Found by Using WQMN 1996 1998 Sites 102, 107, and 110. ............. 144

6.1. Comparison of simulated results to modeled data for Segment 2 ........... 159

6.2. Comparison of simulated results to measured data for Segment 4 .......... 159

6.3. Comparison of simulated results and measured data for Segment 5. ........ 160

6.4. Comparison of simulated results and measured data for Segment 6. ........ 160

7.1. Comparison of model fits to data for a three variable stepwise model, three
variable factorial model, and PARPS numerical model for each collected
data set. ....................................................... 176

7.2. Comparison of model fits to data for a three variable stepwise model, three
variable factorial model, and PARPS numerical model for each season of
the year ............................................ .......... 177

7.3. Comparison of model fits to data for a three variable stepwise model, three
variable factorial model, and PARPS numerical model for each section of the
lagoon ....................................................... 177

A.1. Minimum, maximum, and mean values used for the model sensitivity tests. .. 180

C. 1. The Kd(PAR) (m-1) values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site ..........................................................193

C.2. The Kd(PAR) (m-') values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site 2. .........................................................194

C.3. The Kd(PAR) (m-') values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site3. ..........................................................195

C.4. The Kd(PAR) (m-1) values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site 4. .........................................................196

C.5. The Kd(PAR) (m-1) values calculated for each grid layer (with 4 being the top
layer), the average value of the layer Kd(PAR)s, and the Kd(PAR) value calculated
using the entire water column for times during a one year, 1998 simulation for
Site 5...........................................................197

LIST OF FIGURES

Figure Page

1.1. Halodule wrightii ................................................. 3

1.2. Syringodiumfiliforme .............................................3

1.3. Halophila englemanii .............................................. 4

1.4. Thalassia testudinum ........................................... .4

1.5. Halophilajohnsonii and Halophila decipiens ............................ 5

1.6. Ruppia maritima ..................................... .......... .5

1.7. The setup for a detector measuring radiance through an angle A. .......... 8

1.8. A 27t PAR sensor for measuring downward irradiance .................... 10

1.9. A 47t PAR sensor for measuring downward irradiance ..................... 11

2.1. Percentage of Kd(PAR) due to chlorophyll a. ........................... 38

2.2. Percentage of Kd(PAR) due to color. ................................. 38

2.3. Percentage of Kd(PAR) due to tripton. ............................... 39

2.4. UF sampling trips 1-6 relationship between Kd(PAR) and TSS ............. 47

2.5. UF sampling trips 7-12 relationship between Kd(PAR) and TSS ............ 48

2.6. WQMN 1996-1998 relationship between Kd(PAR) and TSS ............... 49

2.7. WQMN 1999 relationship between Kd(PAR) and TSS. ................... 50

2.8. WQMN 1996-1998 relationship between turbidity and TSS. ............... 50

2.9. WQMN 1999 relationship between turbidity and TSS ..................... 51

2.10. HBOI year 1 relationship between Kd(PAR) and TSS. .................... 52

2.11. HBOI year 1 relationship between turbidity and TSS. ..................... 53

2.12. HBOI year 2 relationship between Kd(PAR) and TSS ..................... 53

2.13. HBOI year 2 relationship between turbidity and TSS. ..................... 54

5.1. Model results for all data sets using Ft. Pierce coefficients. ............... 109

5.2. Model results for all data sets using Marker 198 coefficients. ............. 109

5.3. Model results for SERC data set using Ft. Pierce coefficients. ............. 110

5.4. Model results for SERC data set using Marker 198 coefficients. ........... 110

5.5. Model results for UF synoptic trips 1-6 using Ft. Pierce coefficients......... 111

5.6. Model results for UF synoptic trips 1-6 using Marker 198 coefficients ....... 111

5.7. Model results for UF synoptic trips 7-12 using Ft. Pierce coefficients........ 112

5.8. Model results for UF synoptic trips 7-12 using Marker 198 coefficients. ..... 112

5.9. Model results for WQMN 1996 1998 using Ft. Pierce coefficients. ........ 113

5.10. Model results for WQMN 1996-1998 using Marker 198 coefficients. ....... 113

5.11. Model results for WQMN 1999 using Ft. Pierce coefficients ............. 114

5.12. Model results for WQMN 1999 using Marker 198 coefficients. ............. 114

5.13. Model results for HBOI Year 2 using Ft. Pierce coefficients .............. 115

5.14. Model results for HBOI Year 2 using Marker 198 coefficients. ............ 115

5.15. Model results for January March data using Ft. Pierce coefficients. ........ 118

5.16. Model results for April June data using Ft. Pierce coefficients ........... 118

5.17. Model results for July September data using Ft. Pierce coefficients. ....... 119

xvii

5.18. Model results for October December data using Ft. Pierce coefficients. .... 119

5.19. Model results for the south section of the IRL using Ft. Pierce coefficients. .. 121

5.20. Model results for the middle section of the IRL using Ft. Pierce
coefficients. .................................................. 122

5.21. Model results for the north section of the IRL using Ft. Pierce coefficients. .. 122

5.22. Model results for Banana River using Ft. Pierce coefficients .............. 123

5.23. Model results for Mosquito Lagoon using Ft. Pierce coefficients. .......... 123

5.24. Graph of Equation 4.10. Circles are the Ft. Pierce Inlet data, and squares
are the Marker 198 data. ......................................... 124

5.25. Model results for all data sets using SERC Monte Carlo coefficients. ....... 129

5.26. Model results for the SERC data set using SERC Monte Carlo
coefficients. .....................................................129

5.27. Model results for UF synoptic trips 1-6 using SERC Monte Carlo
coefficients. .............................................. .... 130

5.28. Model results for UF synoptic trips 7-12 using SERC Monte Carlo
coefficients. ................................................. 130

5.29. Model results for WQMN 1996-1998 using SERC Monte Carlo
coefficients. ..................................... ............ 131

5.30. Model results for WQMN 1999 using SERC Monte Carlo coefficients. ..... 131

5.31. Model results for HBOI Year 2 using SERC Monte Carlo coefficients. ...... 132

5.32. Model results for January March data using SERC Monte Carlo
coefficients. ................... ................................. 134

5.33. Model results for April June data using SERC Monte Carlo coefficients. ... 135

5.34. Model results for July September data using SERC Monte Carlo
coefficients ...................... .............................. 135

xviii

5.35. Model results for October December data using SERC Monte Carlo
coefficients. ................................................. 136

5.36. Model results for the south section of the IRL using SERC Monte Carlo
coefficients................................................. 138

5.37. Model results for the middle section of the IRL using SERC Monte Carlo
coefficients. ............................................ ........ 138

5.38. Model results for the north section of the IRL using SERC Monte Carlo
coefficients..................................................139

5.39. Model results for Banana River using SERC Monte Carlo coefficients....... 139

5.40. Model results for Mosquito Lagoon using SERC Monte Carlo coefficients. .. 140

5.41. Graph of Equation 4.10. Circles are the Ft. Pierce Inlet data, and
squares are the Marker 198 data. The solid line represents the curve
fitting the SERC "Monte Carlo" coefficients .................... . 141

5.42. Bottom sediment size (D50) from south to north in the IRL. ............... 142

6.1. Simulated TSS results used for calculating the light attenuation coefficient
for each i, j location in the grid including water quality and TSS loading. .... 149

6.2. Simulated Chlorophyll a results used for calculating the light attenuation
coefficient for each i, j location in the grid including loading of water
quality and TSS .................................................. 150

6.3. Interpolated color values with loading used for calculating the light
attenuation coefficient for each i, j location in the grid including. .......... 151

6.4. Depth of grid used to calculate the light attenuation coefficient, light at
the bottom of the grid, and percentage of incident light reaching the
bottom ... ................................................. 152

6.5. Simulated Kd(PAR) values throughout the IRL for a model run including
loading ........................................................ 153

6.6. Simulated amount of light reaching the bottom of the grid for the case
including loading. ....................................... ..... 154

6.7. Simulated percentage of incident light reaching the bottom of the grid
for the loading case. ............................................. 155

6.8. IRL segment locations............................................. 157

6.9. One year time series plot of simulated TSS concentrations for segments
1-4 for three loading cases. ....................................... 162

6.10. One year time series plot for simulated TSS concentrations for segments
5-8 for three loading cases. ....................................... 163

6.11. One year time series plots of simulated chlorophyll a concentrations for
segments 1-4 for three loading cases. ............................... 164

6.12. One year time series plots of simulated chlorophyll a concentrations for
segments 5-8 for three loading cases. .............................. 165

6.13. One year time series plots of interpolated color for segments 1-4 for
three loading cases. .................................... ....... 166

6.14. One year time series plots of interpolated color for segments 5-8 for
three loading cases. ............................................. 167

6.15. One year time series plots of simulated Kd(PAR) for segments 1-4 for
three loading cases. ............................................. 168

6.16. One year time series plots of Kd(PAR) for segments 5-8 for three
loading cases. ............................................... .. 169

6.17. One year time series plots of simulated light at bottom for segments
1-4 for three loading cases. ....................................... 170

6.18. One year time series plots of simulated light at bottom for segments
5-8 for three loading cases. ................... ..................... 171

6.19. One year time series plots of simulated percent of incident light at
bottom for segments 1-4 for three loading cases. ....................... 172

6.20. One year time series plots of simulated percent of incident light at
bottom for segments 1-4 for three loading cases. ....................... 173

A.1. Variation of predicted Kd(PAR) values with variations in chlorophyll a
concentration. ................................................. 182

A.2. Variations in predicted Kd(PAR) values due to variations in color. ......... 183

A.3. Variations in predicted Kd(PAR) due to variations in TSS concentration .... 183

A.4. Variations in predicted Kd(PAR) due to variations in TSS concentration .... 184

A.5. Variations in predicted Kd(PAR) due to variations in water depth .......... 184

A.6. Variations in predicted Kd(PAR) due to variations in time of day
between 1000 and 1400. ......................................... 185

A.7. Variations in predicted Kd(PAR) due to variations in time of day between 0800
and 1600. .......................................................185

A.8. Variations in predicted Kd(PAR) due to variations in day of the year. ....... 186

B.1. Monte Carlo results for the SERC data set. ........................... 188

B.2. Monte Carlo results for all data sets combined ......................... 189

C.1. Sites used for vertical grid cell tests. ............................. . 192

C.2. The amount of PAR calculated at each layer in the vertical grid at Site 1
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 198

C.3. The amount of PAR calculated at each layer in the vertical grid at Site 2
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 199

C.4. The amount of PAR calculated at each layer in the vertical grid at Site 3
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 200

C.5. The amount of PAR calculated at each layer in the vertical grid at Site 4
using multiple Ka(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 201

C.6. The amount of PAR calculated at each layer in the vertical grid at Site 5
using multiple Kd(PAR)s and one Kd(PAR) for the entire water column.
Taken at noon on each of the given days of a one year, 1998 model run. ...... 202

xxii

Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

MODELING THE EFFECTS OF HYDRODYNAMICS,
SUSPENDED SEDIMENTS, AND WATER QUALITY ON LIGHT ATTENUATION
IN INDIAN RIVER LAGOON, FLORIDA

By

David Joseph Christian

December 2001

Chairperson: Dr. Y. Peter Sheng
Major Department: Civil and Coastal Engineering Department

Declining water quality due to anthropogenic effects has led to a decrease in seagrass

biomass in coastal waters throughout the world. Seagrass beds are vital components of the

coastal ecosystem providing both food and habitat to many species as well as acting as a

stabilizer for marine sediment. The seagrass beds in the Indian River Lagoon (IRL), a

shallow coastal lagoon along the East Coast of Florida, help to support a fishing industry

with a local impact of a billion dollars a year. A decline in light reaching the seagrass due

to poor water quality is suspected of being the major factor in seagrass loss in the IRL as well

as elsewhere.

In order to better evaluate water management decisions aimed at increased seagrass

growth in the IRL, the University of Florida has been developing an Indian River Lagoon

XX111

Pollutant Load Reduction Model (IRL-PLR). This model integrates component models of

hydrodynamic, water quality, sediment, seagrass, and light attenuation processes. This thesis

focuses on the development of a light attenuation model and its integration into the IRLPLR

model. First five different sets of water quality and light data for the IRL are examined. The

report then evaluates regression, factorial, and numerical light attenuation models in order

to select the best light attenuation component for incorporation into the IRL-PLR model.

Each model includes the known light attenuators: suspended solids, chlorophyll a in

phytoplankton, and color from dissolved organic matter. One, two, and three variable

regression models, as well as a three variable factorial model were developed for each of the

data sets, as well as each of the seasons of the year, and each of five sections of the IRL. The

numerical model was calibrated for each data set, season, and section to test the robustness

of the model and to see if incorporating spatial or temporal variations could improve model

results.

Variations in each of the regression and factorial models make it difficult to find a

single model, or a group of models, to best explain all of the data. One set of coefficients for

the numerical model was found that works well with each of the data sets, seasons, and

sections. The numerical model along with that set of coefficients was then incorporated into

the IRL-PLR model.

xxiv

CHAPTER 1
INTRODUCTION AND BACKGROUND

1.1 Introduction and Background

The Indian River Lagoon (IRL), with more than two thousand identified species, is

one of the most diverse estuaries in the world (Barile et al., 1987). Lying on the East Coast

of Florida between Ponce de Leon Inlet in the north and Jupiter Inlet in the south, the IRL

stretches 341 km with an average depth of 1.2 m and a width varying between 0.4 and 12.1

km (Steward et al., 1994).

Seagrass beds play an important role in the IRL, as in estuaries in general. They are

highly productive and ecologically important habitats as well as important sediment

stabilizers (Zieman, 1982). Seagrass beds provide food for fishes and invertebrates as well

as protection from predators (Zieman, 1982). Because of these functions, the seagrass

meadows in south Florida's coastal areas are possibly the greatest nursery and feeding areas

in the region (Zieman, 1982). The importance of seagrass beds also influences water

management decisions. Because of their sensitivity to water quality conditions, as well as

their far reaching importance throughout the system, seagrass beds can act as a gauge for

short and long term water conditions (Vimstein and Morris, 1996).

While currently there are between approximately 70,000 and 90,000 acres of seagrass

beds in the IRL, this is a decrease from past years (Virnstein and Morris, 1996). Because of

2

their importance to sea life, the IRL seagrass beds are a foundation for the local fishing

industry, which generates about a billion dollars a year (Virnstein and Morris, 1996). This

works out to about $12,000/ year for each acre of seagrass coverage (Virnstein and Morris,

1996).

Seven species of seagrass are present in the IRL, giving it the highest diversity of

seagrass species of any estuary in North America (Dawes et al., 1995; Virnstein, 1995). The

seven species in order of decreasing abundance are:

Halodule wrightii shoal grass
Syringodium filiforme manatee grass
Halophila engelmannii star grass
Thalassia testudinum turtle grass
Halophila decipiens paddle grass
Halophilajohnsonii Johnson's seagrass
Ruppia maritima widgeon grass

Halophilajohnsonii occurs only in the southern portion of the IRL. The other six species are

the six species found in tropical and subtropical estuaries in the western hemisphere

(Virnstein and Morris, 1996). These seagrass species are seen in Figures 1.1 1.7. Figures

are from Florida Department of Environmental Protection (2001).

It is believed that the amount of photosynthetically active radiation (PAR), which is

the portion of light usable by plants, reaching the seagrass beds is the main factor controlling

the health of seagrass beds (Virnstein and Morris, 1996). Light attenuation in the water

column limits the amount of PAR which reaches the seagrass. The main light attenuators in

the water column are the water itself, dissolved yellow substance (color), phytoplankton, and

suspended particulates (Kirk, 1981). A decline in water quality, causing an increase in a light

attenuator, can lead to adverse effects on seagrass health.

Shoal-grass (Halodule wrightii)

Figure 1.1: Halodule wrightii

Manatc-grass
(Syrfnodifu fWfomrtw)

Figure 1.2: Syringodiumfiliforme

Figure 1.3: Halophila englemanii

urtlue-grass
(Thaiass~a testudintom)

Figure 1.4: Thalassia testudinum

S 0lr-qras&

)ohnhon'si Sea-grass
(Halophifa johnson ii)

Paddle-grass
(Ha lophila decipiens)

Figure 1.5: Halophila johnsonii and Halophila decipiens

Figure 1.6: Ruppia maritima

6

The University of Florida, with funding from the St. Johns River Water Management

District (SJRWMD), is developing a pollutant load reduction model for the Indian River

Lagoon (IRL-PLR) to help in making water management decisions (Sheng, 1999). The IRL-

PLR model integrates hydrodynamic, water quality, sediment transport, light attenuation, and

seagrass models in order to predict changes in water quality and seagrass growth due to

changes in nutrient loading. For the reasons outlined above, light attenuation plays a major

role in the seagrass health, and therefore a robust light attenuation component of the model

is vital to the overall success of the IRLPLR model. The goal set forth by the SJRWMD is

to be able to consistently have seagrass growth out to a depth of 1.7 m (Virnstein and Morris,

1996). The light attenuation model is an important tool for finding where this is possible and

what water quality changes are needed in order to allow this to happen. This thesis examines

the available light and water quality data for the IRL along with regression, factorial, and

numerical models in order to select and incorporate a calibrated light attenuation model into

the overall IRL-PLR model.

1.2 Light Definitions

Photon

To better understand what is being discussed here, a few definitions for light are

needed. Light is composed of electromagnetic energy packets called photons. The photons

contain properties of both a wave and a particle in what is known as a wave-particle duality.

Each photon carries a certain amount of radiant energy (Mobley, 1994). The amount of

energy q contained in a photon is related to the frequency of the wave V, and its

corresponding wavelength A by the speed of light c and Planck's

constant = 6.626 x 10-34 J s:

he
q= hv=- (1.1)

When we measure light, what the detector is actually measuring is the radiant energy

or the actual number of photons which are hitting it. Thermal detectors measure the heat

which comes from absorbing the photon's radiant energy. Quantum detectors measure the

number of photons which are hitting them. Quantum detectors were used in this study.

Often a diffuser will be placed in front of the detector so that only certain wavelengths will

be detected. In this case, a diffuser was used so that only wavelengths between 400 nm and

700 nm (the visible spectrum) would be measured.

Radiance

If a tube is put in front of the detector (Figure 1.7), such that the light being measured

is only allowed to enter the detector through a certain angle A Q2 the radiance L is being

measured. The equation which shows this measurement is:

SI; t; A) -Q (J s-' m2 srT1 nm1) (1.2)
L ; AtAAA AA
in which A Q is the amount of radiant energy the detector is exposed to, A t is the time

which the detector is exposed to the light, AA is the area of the diffuser that the light is

passing through to get to the detector, and A A is the wavelength interval which the diffuser

is allowing to pass through. L is shown as a function of. which the location of the

instrument in the water, t is time, E is the direction of the light, and 2 is the wavelength at

the center of the wavelength interval A .

Filter AX

Diffuser AA

Detector
Collecting Tube

Figure 1.7: The setup for a detector measuring radiance through an angle
AQ (Adapted from Mobley, 1994).

If everything on the left side of Equation 1.2 is taken to be infinitesimally small, then

the integral may be taken and Equation 1.2 becomes:

L ; t; A) d (W m-2 sr' nm-1) (1.3)

Radiance can be used to find the other needed radiometric values since it includes all

of the information needed about the light field, such as wavelength, spatial features, temporal

features, and directional features.

Since we want to know how much light is available to plants, it is important to know

how much light is coming down from all angles, not just the small angle A 2 To measure

this, the tube which was in front of the detector in Figure 1.7 is removed allowing light to

reach the diffuser from all angles above it and irradiance is measured.

Downward Radiance

Since this study is only concerned with the light which is coming from the sun, and

not that which is being reflected from the bottom of the estuary, the collectors are setup

facing the water surface in order to measure downward irradiance. The equation for

downward irradiance is then:

AQ
Ed (; t; ) A (W m2 nm-1). (1.4)
AtAAAA

This is the same as the equation which explains radiance, except it now does not include the

angle A 2 since the light being measured is not being confined to just the one small angle.

Irradiance Sensors

There are two types of irradiance sensors. The first is a 2nI sensor as shown in

Figure 1.8. If this type of sensor is pointed upward, then it is measuring spectral downward

plane irradiance. If a beam of light is coming in incident to the sensor, and if the sensor is

of area AA, the entire area, AA, is being illuminated by the beam. If the beam is coming

in at angle 0, then the beam is only illuminating an area of AA cos 0. Since the collectors

are collecting photons from all of the angles between 7t and 27, they are integrating the

radiance L multiplied by Icos0I over all O's between T7 and 27t. For this study in which

sunlight is being considered, poU is used in place of 0. The downward plane irradiance being

measured is then related to the radiance as follows:

2 7r
Ed(x;t;,)= f fL(x;t;0; /;A/)\cos0ssin dW dO (1.5)
0=0o=2r

Diffuser

Filter

Detector

Figure 1.8: A 2n PAR sensor for measuring downward
irradiance (Adapted from Kornick, 1998).

The second type of irradiance sensor is the 4r7 sensor (Figure 1-9). Unlike the 2It

sensor, the 47 will collect photons from all angles equally. In order to just capture the

downward irradiance, a shield ( as seen in Figure 1-9) is needed to block any reflected light

coming up from below. Since all angles are being collected, the measurement is of

spectral downward scalar irradiance, Eod The relationship between this measurement and

the spectral radiance is shown in:

2g ~T/2
E ((;t;2Z) = 2 L(T; t;0; 0; A)sinWWd6
0=o9=o

(1-6)

Since the goal here is to find the light which is available for photosynthesis by

phytoplankton and seagrass, then the concern is with the photosynthetically active radiation

(PAR). Photosynthetically active radiation for phytoplankton includes both visible

Figure 1.9: A 47n PAR sensor for measuring downward irradiance.

wavelengths and near ultraviolet wavelengths. Since the near ultraviolet wavelengths are

quickly absorbed in the water column, PAR is usually estimated as just the visible

wavelengths between 400 nm and 700 nm (Mobley, 1994). This estimation is used in this

study.

Downward PAR and Light Attenuation Coefficient

The downwelling PAR reaching the bottom, or any depth in the water column, is

found using the Lambert Beer equation,

Iz = I*exp(-Kd(PAR))*z) (1-7)

12

,where z is the depth below the water surface, Iz is the PAR at depth z, Io is the PAR just

below the water surface, and Kd(PAR) is the light attenuation coefficient for downward PAR

(Dennison et al., 1993). The Lambert-Beer equation follows a negative exponential due to

the nature of light attenuation in water. The wavelengths which are strongly absorbed

disappear quickly as the light enters the water. As the easily absorbed wavelengths

disappear, only the weakly absorbed wavelengths remain (Kirk, 1984). Therefore, if a light

attenuation coefficient is calculated in the upper portion of the water column it will tend to

be higher than if it is calculated, with the same water quality conditions, using a greater depth

(Kirk, 1984).

Kd(PAR) is calculated from PAR measurements in the data by using the rearranged

form of the Lambert-Beer equation,

-K (PAR) = In (1-8)

This rearranged equation can be used to calculate Kd(PAR) using two measurements of PAR,

Iz and I, a distance of z depth apart. It can also use multiple points to calculate Kd(PAR) as

the slope of the best fit line resulting from the plot of 1I -) vs z where Io is the uppermost

PAR measurement and Iz is the PAR measurement at corresponding z depth below where Io

is measured.

13

In order to model the amount of PAR throughout the water column, Kd(PAR) is

modeled and then used in Beer's Law along with the PAR at the water's surface to calculate

PAR at the desired depths.

1.3 Seagrass and PAR Relationships

The minimum light requirements for submerged aquatic vegetation vary from 4 29%

of the light just below the water surface (Dennison et al., 1993). For comparison, land plants

in shaded areas require only 0.5 2% of the light just under the canopy (Hanson et al., 1987;

Osmond et al., 1983). Phytoplankton and benthic algae also require much lower light levels.

Green algae requires 0.05 1.0 % of incident light, while brown algae requires 0.7 1.5% of

incident light (Luning and Dring, 1979). Crustose red algae requires as little as 0.0005% of

incident light (Littler et al., 1985), while lacustrine and marine phytoplankton need 0.5 -

1.0% of incident light (Parsons et al., 1979; Wetzel, 1975). The higher respiration

requirements of seagrasses have been pointed to as the reason for greater light requirements

for seagrasses than for phytoplankton (Dennison, 1987).

Light requirements vary between species. Halodule wrightti and Syringodium

filiforme have been found to each require 17.2% of incident light in Florida (Dennison et. al.

From personal communication with W. J. Kenworthy, 1993). Another report puts the light

requirement for S. filiforme in Florida at 18.3% of incident light (Duarte, 1991). Thalassia

testudinum in Florida has been found to require 15.3% of incident light (Duarte, 1991).

Kenworthy (1993) found much higher light requirements for H. wrightti and S. filiforme. His

results show a minimum of 27% of surface light needed in Jupiter Sound and 35% in Hobe

Sound. The Indian River Lagoon has a mild sloping bottom with a slope of about 2 cm m'

(Kenworthy, 1992). A gentle slope means that such a great range of light requirements could

14

mean a difference of many acres of seagrass. The same is true for changes in Kd(PAR)

(Kenworthy, 1993).

Dennison (1987) found that Zostera marina L. requires an average of 12.3 hours a

day of light above the light compensation point. The light compensation point is the light

level at which the oxygen the plant is getting from photosynthesis is equal to the amount of

oxygen it needs for respiration (Tomasko, 1993).

Duarte (1991) developed a relationship between compensation depth and the light

attenuation coefficient using data for thirty seagrass species and Ruppia. The equation he

developed is:

Z, = 1.86 / K (1-9)

in which Zc is the compensation depth and K is the light attenuation coefficient. This

equation compares well with similar equations. Dennison (1987) found a similar equation

for Zostera marina in the northeast United States. This is shown in Equation

1-10.

Zc = 1.62 / K (1-10)

Nielson et al. (1989) developed a similar equation for Z. marina in Danish estuaries as seen

in Equation 1.11.

Z, = 1.53/K (1.11)

Vicente and Rivera (1982) developed an equation for T. testudinum in Puerto Rican waters.

Their equation is Equation 1.12.

Z = 1.36 /K (1.12)

15

All of these relationships show the strong correlation between the depth at which seagrass

will grow and light attenuation.

More recently, Fong et al. (1997), Cerco et al. (2000), and Burd and Dunton (2001)

have developed seagrass models in which light is a major component in calculating seagrass

growth and death. Fong et al. and Cerco used light in conjunction with salinity, temperature,

and nutrients to model seagrass. Burd and Dunton had their model driven by the light

reaching the seagrass.

1.4 Previous Light Attenuation Models

McPherson and Miller (1994) modeled attenuation in Tampa Bay and Charlotte

Harbor by partitioning Kd(PAR) into portions due to water, color, chlorophyll a, and

nonchlorophyll suspended matter as in Equation 1.13:

k = kw + E2 *C2 + E3 C3 + E4 *C4 (1.13)

where k, is the light attenuation due to water; E2, E3, and E4 are the attenuation coefficients

for dissolved matter, chlorophyll a, and nonchlorophyll suspended matter, respectively; C2

is water color (Pt-Co units); C3 is chlorophyll a concentration (mg m-3); and C4 is the

nonchlorophyll suspended matter concentration (mg m3).

McPherson and Miller (1987) also found the percent contribution of each component

to Kd(PAR) for Charlotte Harbor, Florida. Their findings include non-chlorophyll suspended

matter accounting for 72.5% of Kd(PAR), dissolved matter accounting for 21%, suspended

chlorophyll 4%, and water 3%. Phlips et al. (1995) found percent contributions in Florida

Bay. Their results show non-chlorophyll suspended matter accounting for 75% of Kd(PAR),

chlorophyll containing particles accounting for 14%, color accounting for 7%, and water

accounting for 4%.

16

Hogan (1983) used a model which took into account the Raleigh scattering of photons

by water molecules and Mie scattering from hydrosols as well as absorption. He found that

absorption dominates attenuation for most of the spectrum, except in the visible spectrum,

where scattering becomes most important between 350 nm and 500 nm. While the maximum

transmission of light occurs at 465 nm in clear water, the maximum transmission in turbid

waters occurs at about 550 nm. This is caused by suspended particulate matter absorbing and

scattering more of the shorter wavelengths. Because of this, total transmittance decreases

in turbid waters and the maximum transmittance occurs at the higher wavelengths (Hogan,

1983).

Kirk (1984) used Monte Carlo simulations in order to describe the apparent optical

property of the light attenuation coefficient using the inherent optical properties of absorption

and scattering. Through his Monte Carlo simulations, Kirk developed the equation:

Kd = + G(uo)aba] (1.14)

in which Kd is the vertical light attenuation coefficient for downwelling irradiance, po is the

cosine of the solar zenith angle, a, is the total absorption within the water, and b is the

scattering. G(,uo) is a function of /0 in which:

G() = g,9 g2 (1.15)

where g, and g2 are numerical constants which depend on the optical depth of interest. Kirk

(1984) calculated values for g, and g2 for depths in which the downward irradiance in the

17

water is reduced to 10% of its subsurface value (the midpoint of the photic zone), and for

where downward irradiance is 1% of its subsurface value. Kirk (1991) has found that

Equation 1.14 can be applied to most coastal water bodies studied by oceanographers.

Gallegos developed a physics based model for light attenuation (Gallegos and Correll,

1990; Gallegos, 1993; Gallegos and Kenworthy, 1996). His model uses Equations 1.14 and

1.15 developed by Kirk (1984). The model calculates Kd(PAR) in five nm increments

throughout the wavelength interval of interest. It can be used throughout the visible

spectrum to find the attenuation coefficient for PAR, or can be used for the

photosynthetically usable radiation (PUR) for a certain plant species. a, is found by summing

the absorption by color, chlorophyll a, water, and detritus. Absorption by water is read in

from a file for each wavelength of interest. Absorption due to the other components are

calculated from equations. Scattering, b, is calculated for turbidity. a, and b are then used

to calculate Kd() for each 2 used. Kd), along with incident light at that wavelength are

then used to calculate the light at the depth of interest using the Lambert-Beer equation at

that wavelength. The incident light and light at depth are each integrated over the wavelength

interval of interest and used in a rearranged form of the Lambert-Beer equation to calculate

Kd(PAR) over the wavelength interval. Tests by Gallegos have shown this model to work

as well as Kirk's (Gallegos, 2001).

Gallegos has calibrated and used his model in the Rhode River and Chesapeake Bay

(Gallegos and Correll, 1990). He then calibrated and used the model near Ft. Pierce, FL in

the IRL (Gallegos, 1993; Gallegos and Kenworthy, 1996). The results show a coefficient of

variation of around 15%. He notes, and it is important to remember here as well, that the

18

observed Kd(PAR) values also contain error which contributes to the variation between

modeled and observed values.

There are a few advantages to Gallegos's model. The first is that it is based on

physics with coefficients that can be calibrated to the area of interest. There are only four

coefficients which need to be considered. Three are used to determine the absorption by

detritus, while the fourth is used to calculate absorption by color. The next advantage is that

the use of the Lambert-Beer equation enables depth to be included in the calculation. The

model used by McPherson and Miller does not allow for this. Another advantage to

Gallegos's model is that it can easily be adapted to calculate the attenuation coefficient for

PUR as opposed to PAR for use with a specific plant species.

1.5 This Study

Two approaches have been taken here to finding the best model for Kd(PAR) given

the current data sets. The first approach has been to develop a numerical model based on the

work of Gallegos (1993) in the Indian River Lagoon. The second approach has been to

develop a step-wise regression model using the PROC REG procedure in SAS software. For

both of these approaches, total suspended solids, chlorophyll a (chl_a), and color were used

in the prediction of Kd(PAR).

Chapter 2 describes the data sets used in this thesis. It also gives the statistics on the

data sets used. Chapter 3 shows the regression models developed for the different data sets,

segments of the IRL, and different seasons of the year. Chapter 4 outlines the numerical

model used including the equations and background. Chapter 5 takes that one step further

and describes the stand alone light attenuation model used for testing. This also includes

calibration which was done for the model and results of test runs. Chapter 6 explains the

19

coupling of the light attenuation model to the rest of the IRLPLR model. It includes results

of runs for 1998 with regular loading of nutrients and zero loading of nutrients. Chapter 7

includes discussion and conclusions for this thesis.

CHAPTER 2
DATA SETS

2.1 Introduction

Data sets from five sources are used in calibration and verification of the IRL-PLR

light attenuation model. All five data sets include both light data as well as water quality

data. The five data sets include data taken by Gallegos of the Smithsonian Environmental

Research Center (SERC) for calibration of his numerical model (Gallegos, 1993), data

collected by UF during twelve synoptic sampling trips in 1997-1998, Water Quality

Monitoring Network Data (WQMN) received from SJRWMD, and data collected by Hanisak

at Harbor Branch Oceanographic Institute (HBOI). Data collected Phlips (2000) for the IRL-

PLR project are also used.

2.2 Sampling Procedures

The following section outlines the sample sites for each of the data sets. When

available, equipment used for sampling are also shown. Data from the different groups cover

1994- 1999.

2.2.1 SERC Data Set

Gallegos (1993) sampled light and water quality concurrently near Ft. Pierce Inlet

for calibration of a light attenuation model for the southern part of the IRL. No set frequency

was used for the sampling, but sampling occurred over several days in December, 1992; and

March and April of 1993.

21

Light sampling was done measuring downwelling PAR using 27t Licor 192B

underwater quantum sensors. Sampling was done over the visible spectrum, with the

spectrum being divided into 5 nm increments by interference filters. A deck cell on board

the boat was used to normalize each channel of the spectral radiometer (Gallegos, 1993a).

Vertically integrated water samples were used for the water quality. They were sampled

using a 2 liter Labline Teflon bottle. For sampling, the bottle was slowly lowered, and then

brought back up more rapidly than it could fill. An initial sample was used for rinsing in

the field. Once rinsed, multiple samples were taken each day at each station. The laboratory

methods used were submitted to the FDEP in a Research Quality Assurance Plan by Gallegos

(1993a). The locations for SERC sampling are shown in Table 2.1, while the water quality

sampling relevant to the light attenuation model is shown in Table 2.2.

Table 2.1: Sample sites used in the SERC study.
Site Latitude N Longitude W Northing UTM Easting UTM
(m) (m)
Ft. Pierce Inlet 270 28'06.0" 800 19' 51.0" 3038522 566137
Taylor Creek,
Near Channel
Marker 184

Near Channel 270 22' 16.8" 800 16'38.4" 3027807 571486
Marker 198

Near an Inlet 270 28'03.6" 800 18'58.8" 3038456 567570
Range Marker

Taylor Creek Furthest location upstream that could be reached. Designated
Upstream C-25 C-25 since Taylor Creek receives flow from canal structure C-25.

Channel Marker Near the entrance to Harbor Branch Oceanographic Institute.
172

Near Marker 186 Near Ft. Pierce Inlet in turning basin.

Table 2.2: SERC water quality variables used in the light attenuation model.
Variable Collection Method Units Symbol

Color Niskin Bottle Pt Units color
Total Suspended Solids Niskin Bottle mg/L TSS
Turbidity Niskin Bottle NTU turb
Chlorophyll a Niskin Bottle pLg/L chl_a

2.2.2 UF Data Set

UF conducted twelve synoptic sampling trips between April, 1997 and May, 1998

(Sheng and Melanson, 1999). The first six trips were done at a frequency of twice a month.

The second six were done at a frequency of about once a month. In the first six sampling

trips, forty-five sites were sampled during each trip. Thirty sites were sampled during each

of the second six trips. Sampling included light measurements using three 4-t submersible

Licor sensors with the data stored in Licor dataloggers. It also included in situ water quality

sampling using Hydrolab datasondes as well as bottle samples which are analyzed in the

laboratory. Laboratory bottle samples were collected using a modified Niskin bottle (Sheng

and Melanson, 1999) And transported within 24 hours to the laboratory for analysis.

Light data and water quality sampling were always done at the same time. Vertical

positions of the water quality sampling were consistently at 20% and 80% of the total depth,

while those for the light measurements varied between sampling trips. For the first trip,

measurements were taken simultaneously just below the surface and at 20% of total depth,

then simultaneously at just below the surface and 50% of total depth, and then

simultaneously at just below the surface and at 80% of total depth. Three replicates of each

were taken about a minute apart. For trips two through five, all three Licor sensors were

23

deployed at once. One at 20% of total depth, one at 50% of total depth, and one at 80% of

total depth. Again, at least three replicates were taken when possible. For the final seven

trips, light measurements were taken simultaneously atjust below the surface, at 50% of total

depth, and at 80% of total depth. Once again, three replicates were done with a minute

between each, when possible.

Table 2.3 shows the sampling date for each and every UF sampling trip. Table 2.4

contains the sampling information for relevant light attenuation model variables. Table 2.5

Table 2.3: UF synoptic sampling trips were carried out on these dates.
Trip Number Date of Trip Julian Date

1 April 8, 1997 98

2 April 25, 1997 115

3 May 6, 1997 126
4 May 20, 1997 140

5 June 9, 1997 160

6 June 25, 1997 176

7 November 20, 1997 324

8 January 29, 1998 29

9 February 26, 1998 57

10 March 26, 1998 85

11 April 30, 1998 120

12 May 28, 1998 148

Table 2.4: UF water quality variables used in the light attenuation model.
Variable Collection Method Units Symbol

Color Niskin Bottle Pt Units color
Total Suspended Solids Niskin Bottle mg/L TSS
Chlorophyll a Niskin Bottle mg/m3 chl_a

Table 2.5: Sample sites used during UF synoptic sampling trips.
Site Number Site Number Latitude N Longitude W Northing UTM (m) Easting UTM (m)
Trips7-12 Trips 1-6
1 1 270 55' 54" 80o 31'21" 3089768 546981
2 3 27058' 51" 80032' 12" 3095209 545566
3 6 280 02' 48" 80034' 27" 3102488 541852
4 9 28007' 27" 80036'33" 3111062 538385
5 11 28010'21" 80038'12" 3116408 535668
6 14 28014' 21" 80040'03" 3123785 532621
7 15 280 15'45" 80040'42" 3126367 531551
8 13 28012' 51" 80039'21" 3121037 533773
9 8 28006'00" 800 35'54" 3108388 539458
10 2 27057'27" 80031'36" 3092628 546560
11 16 28017' 09" 80o41'27" 3128949 530318
12 19 28021'39" 80o43'22" 3137250 527161
13 22 28026'21" 80044'51" 3145923 524709
14 24 28029'06" 80045'48" 3150997 523165
15 28 28032'36" 80 46' 18" 3157458 522337
16 31 28034'30" 80o45'39" 3160876 523390
17 30 28034' 12" 80o46'54" 3160411 521354
18 29 28032'51" 80o44'30" 3157926 525271
19 21 28024'43" 80044'26" 3142915 525402
20 17 280 18' 25" 80042'00" 3131310 529414
21 42 28045' 21" 80049'33" 3180992 517004
22 44 28044'03" 80047'33" 3178597 520262
23 40 28043' 18" 80048'51" 3177208 518149
24 39 28041'57" 80047' 15" 3174720 520758
25 37 28040'09" 80048'36" 3171392 518565
26 35 28037' 24" 80048' 00" 3166316 519551
27 33 280 35' 48" 80047'57" 3163362 519637
28 36 28038' 39" 80 48'27" 3168624 518814
29 38 28041' 09" 80o48'48" 3173239 518237
30 45 28043' 37" 80045'49" 3180992 517004

Table 2.6: Additional sampling sites used during UF sampling trips 1-6
Site Number Latitude N Longitude W Northing UTM (m) Easting UTM (m)
4 280 00' 18" 800 32' 45" 3097883 544655
5 280 01' 24" 800 33' 36" 3099909 543255
7 280 04' 30" 800 35' 09" 3105624 540696
10 280 08' 51" 800 37'21" 3113643 537068
12 280 11' 39" 800 38' 36" 3118807 535007
18 280 19' 57" 800 42' 36" 3134133 528427
20 280 23' 21" 800 43' 54" 3140387 526273
23 280 27' 48" 800 45' 06" 3148600 524313
25 280 29' 21" 800 44' 39" 3151463 525041
26 28030' 45" 80046' 24" 3154043 522181
27 280 31' 00" 800 45' 36" 3154507 523485

2.2.3 WOMN Data

Data was also obtained from the Water Quality Monitoring Network (WQMN). The

WQMN, coordinated by SJRWMD, involved sampling monthly at thirty-four sites

throughout the lagoon. Each sampling run collects between two and six samples at each

location over a three day period. Care is taken in the light modeling to use light and water

quality data which were taken at the same time on the same day at the same site.

Data used for this analysis were taken between March 1996 and May 1999. For

reasons discussed later, these data are split into two data sets. The first data set includes

1996 -1998, while the second data set contains data collected in 1999. The locations for the

WQMN sample sites are shown in Table 2.7

2.2.4 HBOI Data

Hanisak at Harbor Branch Oceanographic Institute sampled at seven sites throughout

the IRL between 1994 and 1995. PAR measurements were made every 15 minutes using

both 2xt and 4t Licor sensors. The sensors were deployed at the top and middle of the

seagrass canopies at the sampling sites. Water quality measurements were made weekly.

Care was taken to use only corresponding light and water quality measurements for model

calibration. A detailed account of HBOI sampling procedures is available in their Florida

Department of Environmental Protection (FDEP) Quality Assurance and Quality Control

Table 2.7: Sites sampled during WQMN sampling trips.
Sample Latitude N Longitude W Northing UTM (m) Easting UTM (m)
Site
B02 28026'01" 80038'22" 3145321 535330
B04 28022'00" 80038'00" 3137907 535951
B06 28017'00" 80038'00" 3128675 535979
B09 28011'56" 80037'32" 3119323 536771
CCU 28004'39" 80036'08" 3105884 539105
EGU 280 07'25" 800 37'50" 3110983 536305
GUS 27028'05" 80032'41" 3093780 544800
HUS 28009'55" 80038'31" 3115595 535173
102 28044'20" 80048'02" 3179103 519496
107 28036'12" 80047'54" 3164086 519739
110 280 30'04" 80046'08" 3152768 522639
113 28023'34" 80044'10" 3140773 525873
116 280 16'40" 80040'36" 3128048 531731
118 28011'40" 80038'56" 3118824 534482
121 28007'30" 80037'00" 3111141 537669
123 280 04'12" 80035'40" 3105056 539871
127 27056'44" 80031'46" 3091293 546312
IRJ01 27047'48" 80026'56" 3074834 554311
IRJ04 27041'33" 800 23' 14" 3063324 560443
IRJ05 27039'28" 800 22'32" 3059484 561613
IRJ07 27037'11" 80022'04" 3055272 562401
IRJ10 27041'57" 80023'39" 3064059 559754
IRJ12 27036'34" 80022'01" 3054134 562489
ML02 28043'35" 80043'05" 3177735 527556
SUS 27051'15" 80029'29" 3081185 550098
TBC 28049'14" 80051'41" 3188142 513546
TUS 28001'58" 80034'48" 3100937 541305
V05 29000'29" 80054'34" 3208910 508841
V11 28057'09" 80050'41" 3202762 515153
V17 28052'41" 80050'22" 3194515 515678
VMC 27038'57" 80024'08" 3058517 558987
VSC 270 36'17" 800 22'58" 3053603 560930

27

(QAQC) manual. The HBOI sample information is shown in Table 2.8 and the sample sites

are shown in Table 2.9.

Table 2.8: HBOI water quality variables used in the light attenuation model.
Variable Collection Method Units Symbol

Color Niskin Bottle Pt Units color
Total Suspended Solids Niskin Bottle mg/L TSS
Turbidity Niskin Bottle NTU turb
Chlorophyll a Niskin Bottle pg/L chl_a

Table 2.9: Sample sites used during the HBOI study.
Site Name Site Latitude N Longitude W Easting Northing
Symbol UTM (m) UTM (m)

Banana BR 280 30' 21" 800 35'20" 540242 3153359
River

Melbourne MB 290 09' 01" 80038' 07" 535489 3224728

Turkey TC 28001'52" 800 34'35" 541655 3082043
Creek

Sebastian SN 270 51' 42" 800 29' 31" 550036 3082043
North

Sebastian SS 270 51' 00" 800 29' 18" 550392 3080734
South

Vero Beach VB 270 34' 51" 800 21' 50" 562791 3050990

Link Port LP 270 32' 10" 800 21'00" 564182 3046047

2.2.5 Phlips Data

Phlips sampled twenty-four sites throughout the lagoon during three sampling trips

in July, October, and November of 1999. Light sampling was done using a Licor PAR

quantum sensor. Only data collected during the October trip are used in this analysis since

only samples taken during this trip included TSS for use in the light attenuation model.

2.3 Data Set Statistics

The following are the statistics for each of the data sets used in this study. The

maximum and minimum values as well as means and standard deviations are given for the

model attributes of each data set.

2.3.1 SERC Data Set

Table 2.10 shows the statistics for Gallegos's SERC data set. This is the data set

used by Gallegos for calibration of his light attenuation model in the southern partof the IRL.

The higher color numbers are associated with the outflow from Taylor Creek, which contains

outflow from Canal Structure 25. The color in this area was sometimes seen as a lens of

color in the upper half meter of the water column (Gallegos, 1993).

Table 2.10: Data set statistics for the data collected during the SERC study.
Variable Minimum Maximum Mean Standard
Deviation

Turbidity (NTU) 1.40 6.40 3.00 1.18

TSS (mg/L) < 5.00 28.60 10.71 4.94

Chlorophyll a (gg/L) 1.11 30.77 6.18 6.27

Color (Pt Units) < 7.00 94.00 26.34 25.59

Kd(PAR) (m1) 0.55 2.47 1.27 0.46

2.3.2 UF Data Sets

The UF data are divided into two data sets. The first includes data collected during

synoptic sampling trips 1-6, while the second includes data collected during synoptic

sampling trips 7-12. This division of data sets is for a few reasons. The first six synoptic

trips took place over a three month span in the spring of 1997. The second six synoptic

tripstook place over a seven month span beginning in November, 1997. As explained earlier,

the light sampling techniques varied during the first six trips, but were all uniform during the

second six. One lab was used for sample analysis during the first six sampling trips, but a

different lab was used during the second six trips. For these reasons, it is logical to divide

all of the UF data into these two data sets. The statistics for each of these data sets are given

in Tables 2.11 and 2.12.

Table 2.11: Statistics for the data collected during UF synoptic sampling
trips 1-6.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 55.00 7.88 6.50

Chlorophyll a ([lg/L) < 1.00 20.30 5.26 2.84

Color (Pt Units) < 7.00 26.00 14.72 3.21

Kd(PAR) (m-1) 0.05 4.62 1.02 0.64

The greatest differences between these two data sets are in TSS and color values. In

both instances, the data from trips seven through twelve have higher maximums and means.

The interesting point to be made here is that even though both the color and the TSS mean

30

values are higher during the second six trips, the mean Kd(PAR) value is about the same.

This will be discussed more later.

Table 2.12: Statistics for the data collected during UF synoptic sampling trips 7-12
without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) 9.24 120.50 30.58 16.34

Chlorophyll a (tg/L) 1.38 31.80 7.22 4.81

Color (Pt Units) 10.00 90.00 22.46 14.00

Kd(PAR) (m1) 0.33 2.97 0.97 0.45

2.3.3 WOMN Data Set

As described earlier, this study uses data collected by the Water Quality Monitoring

Network between 1996 and 1999. This data set has been broken into two separate data sets

for the purpose of analyzing the data for the light attenuation model. The first data set

contains data from 1996-1998. The second contains data from 1999. This split is done to

try and account for much higher TSS values found in the 1999 data.

Tables 2.13 and 2.14 show the large difference between the mean TSS values in the

two data sets. The means for both chlorophyll a and color are comparable. The mean value

for Kd(PAR) during 1999 is only slightly higher than that for 1996-1998, although the mean

TSS is much higher. The mean values of turbidity are comparable. HigherTSS value should

lead to higher turbidity values if the sampling is being done at the same locations with the

same sediment types. This issue of high TSS will also be addressed later.

Table 2.13: Data set statistics for data collected by WQMN from March 1996 through
1998.
Variable Minimum Maximum Mean Standard
Deviation

Turbidity (NTU) < 1.00 77.40 5.23 5.25

TSS (mg/L) < 5.00 157.33 13.28 14.02

Chlorophyll a (pg/L) < 1.00 49.68 7.58 6.49

Color (Pt Units) <7.00 85.00 24.23 12.12

Kd(PAR) (m1) 0.24 3.99 1.07 0.53

Table 2.14: Data set statistics for data collected by WQMN between March and May
1999 without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

Turbidity (NTU) < 1.00 43.00 7.74 5.10

TSS (mg/L) 13.60 135.00 62.96 26.46

Chlorophyll a (pg/L) 1.34 14.87 5.88 3.04

Color (Pt Units) 10.00 52.00 21.83 8.40

Kd(PAR) (m1) 0.43 2.49 1.28 0.55

2.3.4 HBOI Data Sets

The Harbor Branch data is split into two data sets for a couple of reasons. The first

is that when we received the data, we received one year at one time and then the second year

at another time. Since both years had a large amount of data, it was decided to keep them

separate. The other reason is that the time of day when the light sample was taken is an

important input for the numerical light attenuation model. Time of day was not received

32

for the first year's data. Because of this, the first year's data are not able to be used in the

numerical model. By keeping the two year's data separate, the second year's data are able

to be used in the numerical model and thus for comparison with the regression model results

and with numerical model results of other data sets. The first year's data are still used for

the regression model. The statistics for the two years of HBOI data are shown in Tables 2.15

and 2.16.

Table 2.15: Data set statistics for HBOI data collected during HBOI's first sampling year
without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 199.99 57.00 26.86

Chlorophyll a (pg/L) < 1.00 96.22 13.15 12.67

Color (Pt Units) <7.00 128.20 17.63 18.82

Kd(PAR) (m-') 0.04 6.88 1.67 1.31

Table 2.16: Data set statistics for HBOI data collected during HBOI's second sampling
year without transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) 24.01 159.30 67.42 24.02
Chlorophyll a (ig/L) 3.29 79.09 16.54 12.04

Color (Pt Units) <7.00 165.60 19.31 19.66

Kd(PAR) (imn) 0.09 6.59 1.76 1.07

Notice that for each year of sampling by Harbor Branch, the mean values for each of

the variables are similar. Other than for WQMN 1999, the mean TSS values for both years

33

are higher than for the other data sets shown so far. The mean Kd(PAR) values for each year

are also much higher than they are for the other data sets, including WQMN 1999.

2.3.5 Phlips Data Set

The Phlips data set is by far the smallest of the data sets used with only nineteen data

records. This is because only one day of sampling included TSS sampling. The statistics for

this data are shown in Table 2.17.

Table 2.17: Data set statistics for data collected by Phlips during their October 1999
sampling trip in which TSS data were collected.
Variable Minimum Maximum Mean o

TSS (mg/L) 5.40 24.50 14.72 5.59

Chlorophyll a (pg/L) 8.50 28.00 18.49 5.05

Color (Pt Units) 14.00 28.00 20.05 4.21

Kd(PAR) (m-') 0.77 3.63 1.57 0.64

2.3.6 All Data Sets Comparison

The previous section shows that there are great differences between the mean values

of the variables in different data sets. Not only do the mean values of a variable vary

between data sets taken by different groups, but they also vary between data sets taken bythe

same group. Table 2.18 shows the mean values for each variable in each data set for easy

comparison.

UF Trips 7-12 have mean Kd(PAR) values which are in line with the other data sets,

with UF Trips 7-12 having the lowest mean Kd(PAR) value of all of the data sets. As for the

mean color values, UF Trips 1-6 has the lowest mean value of 14.72 Pt. Units, while SERC

Table 2.18: Mean values of variables of interest from each of the data sets used in this
study without transformed TSS data.
Data Set Chlorophyll a Color TSS Kd(PAR)
(__g/L) (Pt Units) (mg/L) (m1)
SERC 6.18 26.34 10.71 1.27

HBOI 1994 13.15 17.63 57.00 1.67

HBOI 1995 16.54 19.31 67.42 1.76

UF Trips 1-6 5.26 14.72 7.88 1.02

UF Trips 7-12 7.22 22.46 30.58 0.97

WQMN 7.58 24.23 13.28 1.07
1996-1998

WQMN 1999 5.88 21.83 62.96 1.28

Phlips 18.49 20.05 14.72 1.57

has the highest mean value of 26.34 Pt. Units. All of the mean values for the other data sets

fall within this relatively narrow range. The chlorophyll a data also fall within a relatively

narrow range between 5.26 pg/L for UF Trips 1-6 and 18.49 Vlg/L for the Phlips data set.

Since we are trying to find relationships that can be used to create a model for

Kd(PAR), some of these mean values do not make sense, such as all of the mean values for

UF Trips 1-6 being lower than the mean values for UF Trips 7-12, except for Kd(PAR). With

this being the case, we need to try to analyze the data sets more to see if these trends are seen

not only for the whole data set, but also for individual samples.

2.4 The Relative Importance of Various Factors for Light Attenuation

As stated earlier, this modeling effort concentrated on predicting K/PAR) using the

important, measurable, water quality parameters of TSS, color, and chlorophyll a

35

concentration. Since the mean values for each of these variables vary between the different

data sets, an analysis was done in order to find the relative contributions of these variables

to the KdPAR).

2.4.1 Equations Used to Calculate K/PAR) Attributable to Each Variable

Using an analysis employed by McPherson and Miller (1994) in Tampa Bay and

Charlotte Harbor, Florida, and by Phlips et al. (1995) in Florida Bay, the contributions to

K/PAR) are found for chlorophyll a, color, nonchlorophyll suspended solids (tripton), and

water. This is shown in Equation 2.1:

Kd( PAR) = Kw + Kchla Kco + Ktrip (2.1)

where K, is the contribution to K/PAR) due to water, Kchl is the contribution due to

chlorophyll a, Kcol is the contribution due to color, and Ktrip is the contribution due to tripton.

K, is taken to be 0.0384 m1- (Lorenzen, 1972), Kchla is calculated by multiplying the

chlorophyll a concentration by 0.016 m2 g-1 (Phlips, personal communication), and Kco, is

calculated by multiplying color by 0.014 pt~' m-' (McPherson and Miller, 1987). There is not

a coefficient for use in finding Krip, therefore it is found by subtracting the other KdPAR)

components from the measured KdPAR) as in Equation 2.2.

Ktrip = Kd(PAR) K K cla- Kc (2.2)

Because Krip must be backed out for this analysis, this is not a method that can be used to

model KdPAR). Also note that tripton is used in this analysis, but it is not included in any

of the data sets. The TSS values included in the data sets include tripton as well as

36

chlorophyll suspended solids. Tripton can be calculated by subtracting chlorophyll a

concentrations corrected for pheophytin from TSS concentrations. Since TSS concentrations

are usually much higher than chlorophyll a concentrations1, tripton concentrations are close

to that of TSS.

Equation 2.1 is able to be used since the attenuation coefficient can be partitioned

into partial attenuation coefficients corresponding to different components of the water body

(Kirk, 1983). Kirk did warn, though, and it should be noted that the nature of each of the

attenuation coefficient contributions can be different between the components. Also, he

warned that KdPAR), and thus the contributions to it by each component are not linear (Kirk,

1983).

2.4.2 Data Set Analysis

After values were found for Khl,,, Kcot, and Krip, each value was divided by KdPAR)

and then multiplied by one hundred in order to find the percent contribution to KdPAR).

Table 2.19 shows the average percentages of KdPAR) due to each component for each data

set.

Except for WQMN 1996-1998 and UF trips 7-12, the other data sets all have tripton

accounting for more than 60% of the light attenuation coefficient. Chlorophyll a accounts

for between 7.80% of KdPAR)for the SERC data set and 16.35% of KdPAR) for the HBOI

Year 2 data set. Color is responsible for between 17.02% of KdPAR) for the HBOI Year 2

data set and 33.63% of KdPAR) for the WQMN 1996-1998 data set.

1 See Table 2.18, remember that TSS has units of mg/L and Chlorophyll a has units of pg/L.

Table 2.19: Percent of Kd(PAR) due to each attenuator in this study.
Data Set Average %Kd(PAR) Average % Kd(PAR) Average % Kd(PAR)
Due to Color Due to Chlorophyll a Due to Tripton

WQMN 33.63 11.27 50.84
1996-1998

WQMN 1999 26.22 8.00 62.17

UF Trips 1-6 25.62 9.56 60.10

UF Trips 7-12 32.84 12.69 49.94

HBOI Year 2 17.02 16.35 63.68

SERC 25.07 7.80 63.74

All Sets 24.04 13.03 59.14

Therefore, for each of the data sets, tripton contributes the most to light attenuation. The

Phlips data set was not used because it is too small.

2.4.3 Percentage of Each Measured K/PAR) Due to Each Variable

Figures 2.1 through 2.3 show how the percent of the light attenuation coefficient due

to color, chlorophyll a, and tripton, respectively, varies over the range of measured K/PAR)

values. Each point on the graph represents the percentage for data measured along with the

KdPAR) value. Notice that color and chlorophyll a both contribute a greater percentage to

the light attenuation coefficient at lower measured values of K/PAR) than they do at higher

measured values of K/PAR), where tripton clearly contributes a higher percentage.

Because of this discrepancy between different K(PAR) values, further analysis was

done to see what the relative contribution of each component is to the higher and lower

measured KdPAR) values. The average values for the percentage of K(PAR) due

100- ---------
0
W 90
90
0 80 0
0 70 x
*1) 6 0 --- L-- D --- 0 ---------------------
0 0
S60 8 o
S50- 0
0" 40 -j ^ a n o------------
S30 4 x
2 30 C o 0

20 %-o o ----
0 00
o 0 so o 0 I o0
0 a
0 1 2 3 4 5
Kd(PAR) (m-1)

Figure 2.1: Percentage of Kd(PAR) due to chlorophyll a.

120

a xx x x
O
100 a
O 1o
Sx
Y x x

80 x 2
0 0

20 0 x 0 -0 0

2 3 4 5
Observed Kd(PAR) (m1)

Figure 2.2: Percentage of Kd(PAR) due to color.
20

Figure 2.2: Percentage of Kd(PAR) due to color.

6 7

6 7

120
=WQMN 1996-1998
C100 o WQMN1999

40 HBOI Year 2

Soo
02 -^ ---- -.---I-- 4 --I5 ----I ;

0 0
0I-- 60. .,, -^----, --------x---UF---7-12---

S-40:

-80
SKd(PAR) (m-1)

Figure 2.3: Percentage of Kd(PAR) due to tripton.

to color, chlorophyll a, and tripton for each data set above and below K/PAR) equal to 1.00

m', as well as above and below the average K/PAR) for each data set are shown in Tables

2.20 and 2.21.

KdPAR) equal to 1.00 m-' is chosen as a cutoff here because examination of Figures

2.1 and 2.2 show curves in the plots around this point. Another reason is because this is

about the point where, in some cases, the numerical model (described in Chapters 4 and 5)

goes from over predicting K/PAR) to under predicting K/PAR). The mean K(PAR) value

for each data set is chosen as a cutoff in order to see if there is a difference in data for the

upper and lower K/PAR) values of the data set. Tables 2.20 and 2.21 show that for higher

KdPAR) values, the average percentage of K/PAR) due to tripton is higher than for the lower

KdPAR) values. The exception is the SERC data set. This is because of the high color

values during some of the SERC sampling. For color and chlorophyll a, the average

Table 2.20: Percentage of K/PAR) due to color, chlorophyll a, and tripton for each data set for K(PAR) values above and below
1.00 m1.
Data Set % K/PAR) Due to Color % K/PAR) Due to Chl_a % K(PAR) Due to Tripton

Kd/PAR) < 1 KjPAR) > 1 KdPAR) < 1 K(PAR) > 1 K/PAR) 1 KdPAR) > 1
WQMN 1996-1998 38.11 28.18 11.54 10.95 44.89 58.09

WQMN 1999 35.82 20.01 9.54 7.00 49.41 70.42

UF Trips 1-6 30.14 14.65 10.79 7.12 53.50 75.40

UF Trips 7-12 33.67 30.97 13.98 9.74 47.05 56.50

HBOI Year 1 20.30 14.12 17.57 12.43 55.99 71.33

HBOI Year2 24.35 15.37 22.00 15.08 47.18 67.41

SERC 14.35 31.06 6.47 8.54 74.57 57.68

All Sets 30.76 19.00 13.67 12.56 49.92 66.06

Table 2.21: Percentage of KdPAR) due to color, chlorophyll a, and tripton for each data set for K/PAR) values above and below the
mean KdPAR) value for each data set.

Data Set Mean Avg % K/PAR) Due to Color Avg % K/PAR) Due to Chl_a Avg % K/PAR) Due to
KdPAR) Tripton

K/PAR) KdPAR) K(PAR) K(PAR) KdPAR) K/PAR)
< Mean > Mean < Mean > Mean < Mean > Mean

WQMN 1.07 37.61 27.59 11.59 10.79 45.50 58.97
1996-1998

WQMN 1.28 32.50 16.53 10.08 4.78 52.84 76.58
1999

UF 1-6 1.02 30.06 14.40 10.77 7.06 53.63 75.75

UF 7-12 0.97 33.80 30.90 14.18 9.63 46.68 56.61

HBOI
HB1 1.67 17.84 13.70 15.89 11.35 61.53 73.54
Year 1

HBOI
HBa 1.76 18.63 14.86 18.47 13.51 58.92 70.08
Year 2

SERC 1.27 17.93 35.14 6.71 9.33 71.22 53.18

All Sets 1.31 28.64 17.05 13.43 12.44 52.95 68.54

42

percentage of KdPAR) due to each of those is generally higher for the low KdPAR) values

than for the higher K(PAR) values. Of course, the exception again is the SERC data set. A

portion of the SERC data set was collected near Taylor Creek, which contains outflow from

a canal structure. Data from the Taylor Creek area show higher color data including an

occasional lens with high color values on the surface of the water.

In previous studies using this analysis, tripton also accounted for the largest relative

percentage of K/PAR), but color and chlorophyll a varied. Phlips et al. (1995) studied

seventeen sites sampled during 1993 and 1994 in Florida Bay, Florida. The average

percentages for all of the sites together show tripton accounted for approximately 74.28% of

KdPAR), while the chlorophyll containing particles accounted for approximately 14.24% of

KdPAR), and apparent color 7.35%. McPherson and Miller (1987), using samples collected

in Charlotte Harbor, Florida during 1984 and 1985 found on average that tripton accounted

for 72% of the total K/PAR), color accounted for 21%, and suspended chlorophyll accounted

for approximately 4%.

2.4.4 Analysis by Section

The same analysis performed on each of the data sets was also done for each of the

five sections of the IRL used in this study. The five divisions are a South section below

Northing UTM 3111063 m near Eau Gallie River, a Middle section between Northing UTM

3111063 m and Northing UTM 3154507 m just south of where state road 405 crosses the

IRL a North section above Northing UTM 3154507 m, Banana River, and Mosquito

Lagoon. The divisions were made to try to group sample sites according to like sections of

the lagoon and also to have enough data for analysis in each section. As seen in Table 2.22,

43

the results are very similar for each of the sections with tripton contributing the most to the

light attenuation coefficient, followed by color and the chlorophyll a.

Table 2.22: Percent of KdPAR) due to color, chlorophyll a, and tripton for each
section of the IRL.
Section % KdPAR) Due to % K(PAR) Due to % KdPAR) Due to
Color Chl_a Tripton

North 25.08 12.12 58.54

Middle 27.80 12.16 55.67

South 24.17 12.63 60.04

Banana
Banana 22.18 14.85 57.92
River

Mosquito 28.09 10.53 57.48
Lagoon

2.4.5 Analysis by Season

The same analysis was also done for each season in order to see if different

components had different influences at different times of year. The results are shown in

Table 2.23. Again, not much variation is seen between the different seasons. Two things

that are noticed, though, are that the average percentage of KdPAR) due to color goes down

as the year goes on and the average percentage of KdPAR) due to chlorophyll a increases

from the first half of the year to the second half of the year. Data from 1998 show an

increase in chlorophyll a during the fall (Chenxia Qiu, personal communication). In each

season, tripton again contributes the most to the total light attenuation, followed by color and

chlorophyll a.

Table 2.23: Percent of K/PAR) due to color, chlorophyll a, and tripton for each season.
Season % K(PAR) Due to % K(PAR) Due to % K/PAR) Due to
Color Chl_a Tripton
Jan. March 27.14 11.23 57.99

April June 25.10 11.04 59.39

July Sept. 24.35 15.27 56.89

Oct. Dec. 22.45 15.60 58.74

While the preceding analyses show relative contribution of each component to the

total KdPAR) for each data set, it must be remembered that they are approximations. It must

also be remembered that the values for tripton are calculated by subtracting the contributions

to KdPAR) from the other variables from the total K(PAR) from data. This, therefore, does

not come from the actual tripton data. Since tripton is closely related to TSS, these K,,ri may

not follow along well with TSS data either. An example of this may be seen by examining

the two different UF data sets. While the first six UF sampling trips have a mean TSS value

of 7.88 mg/L and the second six sampling trips have a mean TSS value of 30.58 mg/L, the

percentages of K(PAR)due to tripton in each data set are 60.10% and 49.94%, respectively.

This may show a little of two things. The first is that the mean color value for the second six

sampling trips is higher (22.46 Pt. Units, as opposed to 14.72 Pt. Units for the first six trips)

and therefore, using this method of analysis, leaves less K/PAR) to be associated with

tripton. While this may indicate a flaw in this analysis, it also goes against intuition. The

average chlorophyll a values for the two data sets are 5.26 gg/L for the first six sampling

trips and 7.22 lig/L for the second six sampling trips. These are very similar with the average

for the second six trips being slightly higher. Intuition would say that if the amounts of each

45

of the attenuators increase, so should the attenuation, but in this case the average light

attenuation coefficient for the first six trips is 1.02 m-', while for the second six trips the light

attenuation coefficient is 0.97 m''.

2.5 Data Differences

Differences in data sets are inevitable, even when every precaution is taken to

minimize them. Each data set is being collected by different people who may have all been

taught the same exact techniques, but each may do things in slightly different ways when

confronted with the challenges of sampling in the field. Compounding the problem for this

task is not only different people in one group collected data, but different groups collected

data and different labs analyzed the data. Analysis of the processed data for each set showed

differences in the data, particularly total suspended solids (TSS). Some of the most obvious

differences occurred between UF synoptic trips 1-6 and UF synoptic trips 7-12, as well as

between WQMN data sampled before and after March, 1999. The two years of HBOI

sampling also showed higher TSS values, but do not have a source for comparison as the UF

and WQMN data do. Since our goal was to use as much of the available data as possible,

ways were sought to adjust for these differences.

Since the IRL is a shallow estuary, resuspended sediment would be expected to

increase during wind events (Sheng et al., 1992). Suspended sediment would also be

expected to be a main cause of light attenuation (McPherson and Miller, 1987; Phlips et al.,

1994). Therefore, K/PAR) would be expected to show a positive correlation with TSS.

Accordingly, higher TSS values would be expected to correspond with higher K/PAR)

values. This was not found to be the case when comparing different data sets, particularly

when comparing WQMN data collected between 1996-1998 to WQMN data collected in

46
1999, and also UF data collected in the first six synoptic trips to UF data collected during the

second six synoptic trips. While WQMN 1999 data and UF trips 7-12 data contained much

higher TSS numbers than the previous sampling by each group had shown, the average

K/PAR) values were not appreciably higher, which runs counter to expectations.

2.5.1 UF Data

As stated in the previous section, the average KdPAR) value for UF's second six

sampling trips is less than that for the first six sampling trips, despite a higher average TSS

value. The regressions for KdPAR) against TSS for the UF sampling trips 7-12, while very

poor with R2=0.0013, does show a negative relationship for KdPAR) against TSS, as shown

in Equation 2.3.

Kd (PAR) = -0.001 TSS + 0.9968 (R2 = 0.0013) (2.3)

UF sampling trips 1-6 show a positive correlation between K(PAR) and TSS as seen in

Equation 2.4.

Kd(PAR) = 0.0619 TSS + 0.5309 (R2 = 0.40) (2.4)

The graphs of K/PAR) against TSS for both of these data sets are seen in Figures 2.4

and 2.5. To better illustrate the differences between the two data sets, the average TSS value

for UF sampling trips 7-12 (TSS = 30.58 mg/L) is used in the regression for K(PAR) from

UF sampling trips 1-6. The result is a predicted K(PAR) of 2.42 m-n, while the average

K/PAR) for the second six sampling trips is only 0.97 m"1. The result of using the UF 7-12

average TSS value in the equation for sampling trips 7-12 is the same KdPAR) as the average

of 0.97 m-'. This illustrates that if the regression relationship for sampling trips 1-6 is

47

correct, then the K/PAR) values for sampling trips 7-12 should be higher according to the

corresponding TSS values.

2.5.2 WOMN Data

The same discrepancies between TSS K(PAR) equations are seen in the WQMN

data sets, even though the R2 values for the regressions are not as high. While the regression

for K/PAR) against TSS for WQMN 1999 does not have a negative correlation, it does have

a much gentler slope than the regression for WQMN 1996-1998. This is seen in Figures 2.4

and 2.5, where the regression equation for WQMN 1996-1998 is:

Kd (PAR) = 0.0282 TSS + 0.7299 (R2 = 0.22) (2.5)

5.00_________________
.0 y = 0.0619x + 0.5309
R2= 0.3994
4.00

,*3.00

00 ... %
1. 50

1.00 -
0.50 -
0.00 .. .....
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
TSS (mg/I)

Figure 2.4: UF sampling trips 1-6 relationship between Kd(PAR) and TSS.

5.00
4.50
4.00
3.50
.3.00
M 2.50
M 2.00
S1.50
1.00
0.50
fA nf

y = -0.001x + 0.9968
R2= 0.0013

- -- ---- -="""".--,
U U

.UUJ i I I I I
0.00 20.00 40.00 60.00 80.00 100.00
TSS (mg/I)

Figure 2.5: UF sampling trips 7-12 relationship between Kd(PAR) and TSS.

and the regression equation for WQMN 1999 is :

Kd (PAR) = 0.0053 + 0.9472 (R2 = 0.0529) (2.6)

If the average TSS value for WQMN 1999 (TSS = 62.96 mg/L) is used in the WQMN

1996-1998 equation, it predicts a K(PAR) of 2.51 m-1, compared to an average K(PAR) for

WQMN 1999 data of 1.28 m-'. If the average WQMN 1999 TSS value is used in the

WQMN 1999 equation, it predicts the average KIPAR) of 1.28 mi'.

The Turbidity and TSS relationships should also be examined here to see if they

match up well for the WQMN data sets. Figures 2.8 and 2.9 show the relationships for

WQMN 1996-1998 and WQMN 1999, respectively. The regression equation for WQMN

1996-1998 is:

Turbidity = 0.3427 TSS + 1.0217 (R2 = 0.6769) (2.7)

while the regression equation for WQMN 1999 is:

Turbidity = 0.1148 TSS + 2.0551 (R2 = 0.3442). (2.8)

As for the TSS relationships with K(PAR), there are differences between the

Turbidity TSS relationships of each data set. The slope for the WQMN 1999 regression

is about a third of what it is for the WQMN 1996-1998 data set. This means that as the TSS

values increase, the 1996-1998 data indicate a much higher turbidity than the 1999 data

indicate. So, if a TSS value of 50 mg/L is used in both of those equations, the 1996-1998

equation predicts a turbidity value of 18.16 NTU's, while the 1999 equation predicts a

turbidity value of 7.80 NTU's. Turbidity was not measured during the UF sampling trips

so this type of comparison can not be done for those data sets.

5.00
y = 0.028
4.50
4.00

3.00
S2.50 -
2.00 .

E
0.50I-
1.00- ME

0.00
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
TSS (mg/I)

Figure 2.6: WQMN 1996-1998 relationship between Kd(PAR) and TSS.

90.00 100.00

5.00
4.50
4.00
^3.50
1,3.00
C 2.50
0 2.00
S1.50
1.00
0.50
0.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00
TSS (mg/L)

Figure 2.7: WQMN 1999 relationship between Kd(PAR) and TSS.

90.00 100.00

90.00 -----------------------
y = 0.3427x + 1.0217
80.00 R2=0.6769

70.00

p 60.00-
Z
50.00

0 40.00 -

30.00 .

20.0 0 -

10.00 *N7 1

0.00 "
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00

TSS (mg/L)

Figure 2.8: WQMN 1996-1998 relationship between turbidity and TSS.

160.00

y = 0.0053x + 0.9472
R2= 0.0529

U U_ U

----- F. U i ---
------------------------------------------- ---------

90.00
80.00 = 0.1148x + 2.0551
2 = 0.3442
70.00
60.00
I-
Z
50.00

"0 40.00
30.00
20.00 _
0.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)

Figure 2.9: WQMN 1999 relationship between turbidity and TSS.

2.5.3 HBOIData

Both years of sampling by HBOI show relatively high average TSS values with the

average TSS for HBOI Year 1 being 57.01 mg/L and the average for HBOI Year 2 being

67.43 mg/L. The average K/PAR) values are also higher than for the other data sets with

the average K/PAR) for HBOI Year 1 being 1.67 m' and the average for HBOI Year 2 being

1.76 m' To see if these numbers are consistent with any of the trends seen in the other data

sets, the average TSS values for HBOI Years 1 and 2 are used in the K(PAR) TSS and

Turbidity-TSS regression equations of the other data sets. The regression equations for

KdPAR) TSS and Turbidity TSS for HBOI Year 1 are shown in Equations 2.9 and 2.10,

with the graphs being shown in Figures 2.10 and 2.11.

Kd (PAR) = 0.0201* TSS + 0.5057 (R2 = 0.1806) (2.9)

Turbidity = 0.1916 TSS 4.0611 (R2 = 0.5685) (2.10)

52

The regression equations for HBOI Year 2 are shown in Equations 2.11 and 2.12. The

graphs of the relationships are shown in Figures 2.12 and 2.13.

Kd (PAR) = 0.0044 TSS + 1.462 (R2 = 0.0095) (2.11)

Turbidity = 0.1151* TSS + 0.5324 (R2 = 0.2114) (2.12)

The results using average HBOI TSS values in each of the regression equations are

shown in Tables 2.24 and 2.25.

As is seen in Table 2.25, the predictions for K(PAR) using the average TSS

values for HBOI Years 1 and 2 in the K(PAR) TSS regression equation for each data set

7.00 .----- ...... ......... .... .. .. ..... -- ..........
0 = 0.0201 x + 0.5057
6.00 R= 0.1806

^5.00

V4.00
2X 3.00 ---------* -- " " ,--------

13.00 U.

0.00 I
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)

Figure 2.10: HBOI year 1 relationship between Kd(PAR) and TSS.

5 0 .0 0 -..... ....................... ............................ ........... .
45.00 y=0.1916x 4.0611 q
R2 = 0.5685
40.00
s35.00
Z30.00
.25.00
20.00
015.00 -
I-- I
10.00 U- U no ut- -
5.00 -" ,''- i I mI
0.00 ...i--
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)

Figure 2.11: HBOI year 1 relationship between turbidity and TSS.

7.00
y = 0.0044x + 1.462
6.00
00 R2 = 0.0095

S5.00

IN I U *

2.00 4"1 IN* *-

1.00
IN l U U
0.00 -U"
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00
TSS (mg/L)

Figure 2.12: HBOI year 2 relationship between Kd(PAR) and TSS.

50.00
45.00
40.00
'35.00
I.-
Z 30.00
=25.00
20.00
115.00
I--
10.00
5.00
0.00

y =O1151x + 0.5324
R = 0.2114

FAS

%A
U
yl + ,'
U U U
E
:E

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00
TSS (mg/L)

Figure 2.13: HBOI year 2 relationship between turbidity and TSS.

Table 2.24: Turbidity calculations using HBOI years 1 and 2 average TSS values.

Data Set HBOI Year 1 HBOI Year 2 WQMN 96-98 WQMN 1999

HBOI Year 1 6.86 7.09 22.56 8.60

HBOI Year 2 8.86 8.29 24.13 9.80

Table 2.25: K(PAR) calculations using HBOI years 1 and 2 average TSS values.

Data Set HBOI HBOI WQMN WQMN UF 1-6 UF 7-12
Year 1 Year 2 1996-98 1999

HBOI
a 1.65 1.71 2.34 1.25 4.06 0.94
Year 1

HBOI
HBa 1.86 1.76 2.63 1.30 4.70 0.93
Year 2

55

vary greatly. The average K/PAR) value for each HBOI data set is best predicted by the

K/PAR) TSS regression equation for that data set. The K/PAR) TSS equations from the

WQMN 1996-1998 and UF 1-6 data sets, the data sets with lower TSS values, overpredict

the average K/PAR) for the HBOI data, while WQMN 1999 and UF 7-12, the data sets with

higher TSS values, underpredict. This indicates that there are major differences between the

data sets which could cause problems when trying to model all of the data sets at once.

2.5.4 Attempt to Make TSS Data Uniform

The one similarity for both the WQMN and UF data sets is a change of labs for

sample analysis occurred between the separation of data for both sets. One lab did the

analysis for WQMN 1996-1998 and the first six UF sampling trips. Another lab did the

analysis for WQMN 1999 and the second six UF trips2. If it can be assumed that sampling

methods and techniques used by both groups remained the same between sampling trips, then

a closer look at the labs used for sample analysis should be taken.

Split sample analysis was done in order to try and determine if there were differences

between the analyses done by the two labs. Samples were taken at the northern UF inshore

sampling tower at 280 39' 18.36" N latitude and 800 48' 4.02" W longitude at 14:00 EST on

13 April 2000. The samples were taken in a Niskin type bottle at 20% and 80% of the total

depth. One sample for each lab was taken out of the same Niskin bottle sampling with care

being taken to assure uniformity between the samples. Two samples from the upper location

2The changing of labs occurred after UF sampling trip number 6 for the UF data. For the WQMN data the
change took place in October of 1998. While the WQMN data does not show an increase through the end of 1998,
the first data used in 1999 was in March. The reason the jump did not occur in WQMN data for October through
December 1998 is not known.

56

and two from the lower location were each sent to each of the labs. The results are shown

in Table 2.26.

Table 2.26: Results from TSS split sample analysis.
Laboratory Upper Level TSS Value (mg/L) Lower Level TSS Value (mg/L)

Lab 1 17.4 15.8

Lab 2 135.0 36.2

The results for the lower samples are somewhat similar, but the initial results for the

upper samples are extremely different with the number from the second lab being extremely

high. This was brought to the attention of the second lab and the results from the first lab

were revealed. The second lab then redid their calculations and presented a corrected value

of 17.8 mg/L. When asked to see what was done, we did not get a detailed account from the

second lab, but instead a description of what should have been done.

Since these discrepancies did exist, any model which used TSS as an input to try to

predict KdPAR) values would not be able to be calibrated to both of these extremes (an

explanation of the models will appear later). An attempt needed to be made to find a

relationship between the TSS values found by both labs in order to try to convert all of the

TSS data to resemble that of one lab. Since the TSS reported by the first lab had a better

correlation with KdPAR), the numerical model (which will be explained later) was calibrated

using TSS numbers which resemble the first lab results, and there are more data resembling

that from the first lab, it was decided to try to find a way to convert the data from the second

lab to resemble that of the first.

57

The common thread which was found to do this is the turbidity measurements for the

WQMN data. Turbidity data are also analyzed by the labs, but we do not have reason to

suspect major differences in the methods used by the two labs. Therefore, the Turbidity -

TSS relationships shown in Figures 2.8 and 2.9 are used for the conversion. The TSS

numbers for UF synoptic sampling trips 7-12 as well as WQMN 1999 are converted to

turbidity using the Turbidity -TSS relationship for WQMN 1999 data (Eq. 2.8). These

"turbidity" numbers were then used in the rearranged WQMN 1996 1998 Turbidity TSS

relationship to find the converted TSS values.

(Turbidity- 1.0217)
TSS = (2.13)
0.3427

Since the two HBOI data sets also contain high TSS values, the same conversion method

is used in order to make the TSS data more uniform for easier use in the numerical model.

2.6 Data Sets Statistics With Converted TSS Values

This section shows the TSS statistics for the data sets with the high original TSS

values after the conversion using the TSS-Turbidity relationships from WQMN 1996-1998

and WQMN 1999. It also shows the data statistics, including the converted TSS values for

each season and also for the five different sections of the IRL used in this analysis.

2.6.1 Converted TSS Data Sets

The statistics for the converted TSS values are shown in Table 2.27. The other

variables are not shown because they did not change. Table 2.28 shows a comparison

between the original and converted TSS values for each data set. The mean TSS values for

UF sampling trips 7-12, WQMN 1999, HBOI Year 1, and HBOI Year 2 decrease between

58
the original and converted TSS values by 56.64%, 61.72%, 61.21%, and 62.03%,

respectively.

Table 2.27: Transformed TSS statistics using WQMN 1994-1998 and WQMN 1999
turbidity-TSS relationships;
Data Set Minimum TSS Maximum TSS Mean TSS Standard Deviation
(mg/L) (mg/L) (mg/L) (mg/L)
UF 7-12 6.11 43.38 13.26 5.47

WQMN 7.57 48.24 24.10 8.86
1999

HBOI 1 3.02 70.01 22.11 9.00

HBOI 2 11.06 56.38 25.60 8.05

2.6.2 Seasons Statistics

All of the data sets are combined for use in the data sets for each season. The seasons

are divided into four three month data sets. The first division is January March,the second

one is April June, the third is July September, and the fourth is October December. The

statistics for each of these are shown in Tables 2.29 through 2.32.

Examining the mean values, chlorophyll a has the lowest mean concentration during

April June at 6.66 Vg/L and the highest average concentration of 15.32 pg/L during

October December. Color has its lowest mean value of 15.95 Pt. Units during April June

and its highest mean value of 24.76 Pt. Units during October December. The lowest mean

TSS concentration of 14.42 mg/L comes during April June and the highest mean TSS

concentration of 18.46 mg/L comes during October December. As would be expected,

April June, which has the lowest mean values of the other variables, also has the lowest

59
K/(PAR) value of 1.09 m-'. Along those same lines, October December has the highest

mean values for each of the variables and also the highest mean value of KdPAR) of

1.60 m'.

Table 2.28: TSS (mg/L) statistics for data transformed using WQMN 1994-1998 and
WQMN 1999 turbidity-TSS relationships.
Data Set Minimum TSS Maximum TSS Mean TSS Standard Deviation

UF 7-12
UF 72 9.24 120.50 30.58 16.34
Original

UF 7-12
U e72 6.11 43.38 13.26 5.47
Converted

WQMN
1999 13.60 135.00 62.96 26.46
Original

WQMN
1999 7.57 48.24 24.10 8.86
Converted

HBOI 1
HBO1 0.01 199.99 57.00 26.86
Original

HBOI 1
o 3.02 70.01 22.11 9.00
Converted

HBOI 2
Ori 24.01 159.30 67.42 24.02
Original

HBOI 2
HBo2 11.06 56.38 25.60 8.05
Converted

2.6.3 Sections Statistics

The statistics for each of the sections of the IRL are presented here to see if any

noticeable differences are present. This information may be important later for calibration of

the numerical light attenuation model. The statistics are shown in Tables 2.33 through 2.37.

60

For the sections, Mosquito Lagoon has the highest TSS mean value with 23.65 mg/L

while Banana River has the lowest mean TSS value of 13.43 mg/L. Chlorophyll a

concentration is the highest in the South Section with a mean value of 12.39 pg/L and is the

lowest in the Middle Section with a mean value of 7.23 |lg/L. For Color, the highest mean

value occurs in the South Section with a value of 25.02 Pt. Units and the lowest mean value

occurs in the Middle Section with a value of 13.43 Pt. Units. As for the K/PAR) values, the

highest mean value is 1.60 m-1 for the South Section which has the highest mean values for

color and chlorophyll a. It also has the second highest mean TSS value of 19.37 mg/L. The

lowest mean K/PAR) value is 0.94 m-' in the Banana River. The only other variable with the

lowest mean value being in the Banana River is color.

Table 2.29: Statistics for January March with transformed TSS values.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 70.01 16.54 10.97

Chlorophyll a ([pg/L) 1.11 50.55 9.33 7.70
Color (Pt. Units) < 7.00 94.00 21.87 15.41

Kd(PAR) (m-1) 0.09 6.84 1.40 1.04

Table 2.30: Statistics for April June with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 89.50 14.42 10.81

Chlorophyll a (pg/L) < 1.00 37.22 6.66 4.98
Color (Pt. Units) <7.00 69.90 15.95 7.93
Kd(PAR) (m-') 0.05 4.62 1.09 0.65

Table 2.31: Statistics for July September with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 43.20 17.92 9.62
Chlorophyll a (pg/L) < 1.00 68.57 13.36 11.00

Color (Pt. Units) < 7.00 103.60 23.53 17.95
Kd(PAR) (m-1) 0.33 6.88 1.45 0.90

Table 2.32: Statistics for October December with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 43.38 18.46 8.02

Chlorophyll a (pig/L) 1.81 96.22 15.32 13.80

Color (Pt. Units) <7.00 165.60 24.76 22.24
Kd(PAR) (m-') 0.04 6.59 1.60 1.05

Table 2.33: Statistics for the South Section of the IRL with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 70.01 19.37 10.98
Chlorophyll a (pg/L) < 1.00 96.22 12.39 11.09

Color (Pt. Units) < 7.00 165.60 25.02 20.49

Kd(PAR) (m-') 0.04 6.88 1.60 1.01

Table 2.34: Statistics for the Middle Section of the IRL with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 49.00 9.73 7.33
Chlorophyll a ([g/L) < 1.00 35.01 7.23 4.97

Color (Pt. Units) 7.50 70.00 18.22 8.16

Kd(PAR) (m-1) 0.33 3.71 1.00 0.46

Table 2.35: Statistics for the North Section of the IRL with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 55.00 14.74 8.91

Chlorophyll a (l[g/L) < 1.00 68.57 8.96 8.80
Color (Pt. Units) < 7.00 90.00 16.51 9.41

Kd(PAR) (m-') 0.05 6.43 1.23 0.88

Table 2.36: Statistics for the Banana River with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) < 5.00 37.90 16.56 7.39
Chlorophyll a (ig/L) < 1.00 79.09 8.36 9.32
Color (Pt. Units) < 7.00 52.00 13.43 6.41
Kd(PAR) (m') 0.09 6.22 0.94 0.64

Table 2.37: Statistics for the Mosquito Lagoon with transformed TSS.
Variable Minimum Maximum Mean Standard
Deviation

TSS (mg/L) 6.60 89.50 23.65 15.99
Chlorophyll a (pg/L) 1.58 22.90 7.95 6.14
Color (Pt. Units) 11.00 45.00 21.27 8.21

Kd(PAR) (m-1) 0.43 3.16 1.28 0.66

CHAPTER 3
REGRESSION MODELS

3.1 Introduction

One way to try to find a light attenuation model is to find a simple regression

relationship between the Kd(PAR) calculated from light measurements and the water quality

measurements taken simultaneously. This type of empirical model is a simple way to relate

light attenuation to water quality at a certain time. This method was used previously by

McPherson and Miller (1994) in Tampa Bay and Charlotte Harbor.

The water quality parameters used for the regression analysis are total suspended

solids (TSS), chlorophyll a (chl_a), and color. The chlorophyll a concentration is related to

the phytoplankton concentration in the water while the color in the water is related to

dissolved organic matter within the water. These parameters are chosen for three main

reasons. The first is that they are all known light attenuators (Gallegos, 1993). The second

is that they are the same parameters used in the numerical light attenuation model which is

being tested. This enables an easier comparison between the models. The third reason is that

they are recognized as actual light attenuators. An example of the opposite of this would be

using salinity in a light attenuation model for highly colored water coming from a freshwater

source. Here, salinity may be very well correlated with light attenuation, but the color in the

water is what is doing the attenuating, not the salinity. McPherson and Miller (1994) found

a relationship between the light attenuation coefficient and salinity to have a r? = 0.71 in

65

Tampa Bay and Charlotte Harbor, but note that the increase in attenuation comes from an

increase in color, suspended matter, and nutrients causing algal growth.

Using those three parameters, the best one-variable, two-variable, and three-variable

linear stepwise regression models are produced for each of the available data sets using the

PROC REG option available in SAS software (SAS Institute Inc, 1990). Using the stepwise

method means that just because a variable is used in the one-variable model, it does not

necessarily need to be used in the two-variable model, thus allowing for the best model to

be found. In addition, a three-variable, non-linear factorial regression model is also

produced for each data set using the PROC GLM option in SAS software. Whereas the

simple regression models have one coefficient for each variable, as well as an intercept, the

factorial model also includes coefficients for products of the variables. Each model also

includes an R2 value to help judge the fit as well as a p value in order to measure the

significance of each component in the model.

In addition to finding the models for each of the data sets separately, linear regression

and factorial models have been developed for all of the available data together at once. The

combined data were then divided into seasons and sections of the IRL to see if time or space

dependent models would provide better results. Not enough data were available to divide

each separate data set into seasons and sections. The seasonal divisions are January March,

April June, July September, and October December. The sections of the lagoon used

include Banana River, Mosquito Lagoon, a southern section up to Northing UTM 3111063 m

near Eau Gallie River, a middle section between Northing UTM 3111063 m and Northing

UTM 3154507 mjust south of where state road 405 crosses the IRL, and a northern section

north of Northing UTM 3154507 m.

3.2 Regression Model Statistics

In order to understand the analysis used in this chapter, a few terms need to be

defined. The "fit" of the regression model to the data is determined using the coefficient of

determination, r. For a linear regression model using one independent variable and one

dependent variable, r2 indicates the percentage of the total sums of squares that is fit by the

regression model (Weimer, 1987). Weimer (1987) gives a good explanation of just what this

means and how it is calculated.

To see if the regression model that has been calculated is dependable enough to be

used for modeling the dependent variable, a hypothesis needs to be tested. The hypothesis

tested is known as the null hypothesis, Ho. Weimer (1987) defines the null hypothesis as the

hypothesis of "no difference." The null hypothesis for this study is that the model does not

predict KPAR. So for the regression equation in Equation 3.1:

1 = bo + bx (3.1)

the null hypothesis would be that b, = 0 and therefore

5 = bo (3.2).

If this is the case, then each answer for y is bo, no matter what values x is, so x makes "no

difference." If this is the case, then we say:

Y = bo (3.3)

So then we have three different values for y: the observed value, y, the value

calculated by the regression equation, and the result of the null hypothesis, y There is

a deviation between y and y This can be partitioned into the difference between 5 and y,

67

which is the deviation due to the regression, and the difference between y and y which is

the deviation due to error. This is shown in equation 3.4.

y y = (y )- ( y) (3.4)

The sum of the squares of each component satisfies:

S(Y = (Y- )+ )2 (3.5)

where:

sum of squares of y (SSy) = (y y)2 (3.6)

sum of squares for error (SSE) = (y )2 (3.7)

sum of squares for regression (SSR) = ( y)2 (3.8).

Using the above definitions, r2 is defined in:

r2 = SSR/SSy (3.9).

The r2 is used to denote the coefficient of determination since it can be shown to be

the square of the Pearson correlation coefficient, r (Weimer, 1987). A Pearson correlation

coefficient with a value of 0.60 is being taken here to indicate real world significance

(Kornick, 1998). This correlates with a r2 of 0.36. For the cases when more than one

variable is used in the regression equation, the multiple correlation coefficient R2 is used.

In the case of this paper, R2 is used to denote the correlation coefficient for each regression

model, therefore keeping with the same notation as the SAS output.

68

An F distribution is used to determine if the model and each variable in the model are

statistically significant. In order to use an F distribution, first an F statistic must be

calculated. For the regression model, an F statistic is calculated with:

SSR
F 2 (3.10)
Se

where SSR is defined in equation 3.8 and S2 the residual variance, is defined in:

S SSE
s2 (3.11).
e n- 2

where SSE is defined in equation 3.7 and n is the number of points.

The degrees of freedom for the numerator and denominator of Equation 3.10 are

needed since the F distribution is dependent upon degrees of freedom in its constituents. By

definition, the degree of freedom in the numerator is one. The degrees of freedom for the

denominator are n 2. The degrees of freedom as well as the F statistic are then used to find

a probability value (p value) for the model. This p value, when compared to a level of

significance (a) is used to determine if the null hypothesis can be rejected or not. Weimer

(1987) defines the p value as "the smallest level of significance that would have resulted in

Ho being rejected." If the p value is less than a (in this case 0.05), then the null hypothesis

can be rejected and the model is statistically significant.

An F statistic is also calculated for each added variable with Equation 3.12 to see if

the null hypothesis can be rejected for each variable.

AR2/g
F A (3.12)
(1- R2)1(n k 1)

In Equation 3.12, AR2 is the change in R2 with the addition of the new variable, g is the

number of new variables added, n is the number of points, k is the total number of variables

used (Wonnacott and Wonnacott, 1977). In this equation, g are the degrees of freedom in

the numerator and n k 1 are the degrees of freedom in the denominator. These are used

to find ap value the same way as they are for the F statistic for the entire model.

In general, the larger the F statistic is, the smaller the p value is, and therefore the

chances are better of having the model or variable be statistically significant. Because of the

position of the total number of samples, n, in the equations, it can be seen that larger values

of n lead to larger values of F statistics. Therefore, larger data sets have a better opportunity

of having the variables and regression model be statistically significant.

3.3 Regression Models for Various Data Sets

In this section the best one, two, and three variable stepwise regression models as

well as the best three variable factorial model are presented for each individual data set and

for the combined data set. This allows for comparison to see how compatible a model for

one data set may be with another data set.

3.3.1 Best One-Variable Linear Regression Model for Each Data Set

The results for the best one variable model for each data set are shown in Table 3.1. Many

things can be seen just by looking at the results for the best one-variable model. The first,

by looking at the R2 values, is that the SERC data set has the best fitting one-variable model

with R2=0.6824. The best one-variable model for this data set uses color as the variable.

70

This makes sense in that one of the goals of Gallegos using this data set (Gallegos, 1993) was

to be able to investigate the effects of color on light attenuation modeling. Also, this data

set included sampling at Turkey Creek, where a color lens was found on the surface of the

water and was attempted to be modeled. All of the one-variable models for the other data

sets, including the combination of all of the data, are statistically significant to the 0.05 level

except WQMN 1999 and Phlips which are very small data sets (Table 3.2). Of the data sets

in which the TSS values were highest (Harbor Branch Year 1, Harbor Branch Year 2, UF

Trips 7-12, and WQMN 1999) HBOI Year 2 and UF Trips 7-12 do not have TSS as the best

one variable model, but instead use color and chlorophyll a, respectively. Also, even though

only UF Trips 7-12 has chlorophyll a in the model, and five of the eight separate data sets

have TSS, the combination of all of the data sets has a one variable model with chlorophyll

a.

Table 3.1: Best one-variable regression model for each data set.
Data Set Coefficient and Variable Intercept R2
All Sets 0.04085 chl_a 0.90280 0.1935
HBOI Year 1 0.06132 tss 0.31317 0.1776
HBOI Year 2 0.02117 color 1.34719 0.1499
UF Trips 1-6 0.06187 tss 0.53106 0.3994

UF Trips 7-12 0.03594 chl_a 0.70714 0.1492

WQMN 1996-1998 0.02823 tss 0.72991 0.2179
WQMN 1999 0.01610 tss 0.89213 0.0662
Phlips 0.03310 tss 1.07845 0.0838
SERC 0.01479 color 0.88387 0.6824

71

Perhaps the best point that can be made from these results is the variation between

data sets, not only variation in the variables used for each data set's model, but also the

variation between equations in which the same variable is used. This agrees with Kornick's

(1998) findings. Since there is such variation in variables used, we must add another variable

to see if there is an improvement.

Table 3.2: F values and p values for the best one-variable regression models.
Data Set Variable F Value p Value
All Sets Chl_a 302.70 < 0.0001
HBOI Year 1 TSS 35.41 < 0.0001
HBOI Year 2 Color 52.38 < 0.0001

UF Trips 1-6 TSS 158.24 < 0.0001
UF Trips 7-12 Chl_a 24.02 < 0.0001
WQMN 1996-1998 TSS 88.05 < 0.0001
WQMN 1999 TSS 1.98 0.1699
Phlips TSS 1.55 0.2294
SERC Color 109.60 < 0.0001

3.3.2 Best Two-Variable Linear Regression Model for Each Data Set

By adding a second variable to the regression models, the R2 values improve for all

of the data sets as shown in Table 3.3. Again, neither of the variables used in the models for

the Phlips data set nor for the WQMN 1999 data set are statistically significant at the 0.05

level. This is due, at least in part, to the small sizes of each of those two data sets.

As shown in Table 3.4, another interesting note is that the two variable regression

model for all of the data sets combined uses TSS and color (both of which are more

statistically significant with p values of <0.0001), while chlorophyll a is used in the one

72

variable model and is statistically significant at the 0.05 level in that model with ap value

of <0.0001.

Table 3.3: Best two-variable model for each data set.
Data Set Coefficient Coefficient Intercept R2 R2
and Variable and Variable Improvement

All Sets 0.04153 tss 0.02058 color 0.22263 0.3135 0.1200

HBOI
HB1 0.077041 tss 0.03235 color -0.60507 0.3822 0.2046
Year I

HBOI
HBOI 0.01822 color 0.02807 chl_a 0.93994 0.2459 0.0960
Year 2

UF
S1 0.05431 tss 0.04812 chla 0.33744 0.4394 0.0400
Trips 1-6

UF
S- 0.01135 color 0.03681 chlia 0.44584 0.2753 0.1261
Trips 7-12

WQMN 0.02594 tss 0.01649 color 0.35790 0.3592 0.1413
1996-1998

WQMN 0.02081 tss 0.04235 chl_a 0.52962 0.1144 0.0482
1999

Phlips 0.04447 tss 0.03593 color 0.19068 0.1297 0.0459

SERC 0.01495 color 0.01715 chl_a 0.77365 0.7375 0.0551

Using an R2 of 0.36 to determine if the regression model has real world significance,

the two variable models for HBOI Year 1, UF Trips 1-6, and SERC all fit that criterion. In

order to see if any more data sets can have models which fit this criterion, a third variable is

added.

3.3.3 Best Three-Variable Linear Regression Model for Each Data Set

Table 3.5 shows the best three variable linear regression model for each of the data

sets. Again, the addition of another variable improves the R2 of the models for each data set,

73

with the combined data set improving the most (0.0539 to R2 = 0.3674), while others barely

improve at all over the two-variable models (UF Trips 1-6 up only 0.0017 to R2 =

Table 3.4: F values andp values for the best two-variable regression models.
Data Set Variable F Value p Value

All Sets TSS 415.32 < 0.0001

Color 230.79 < 0.0001

HBOI Year 1 TSS 69.97 < 0.0001

Color 53.98 < 0.0001

HBOI Year 2 Color 42.31 < 0.0001

Chl_a 37.66 < 0.0001

UF Trips 1-6 TSS 113.22 < 0.0001
Chl_a 16.93 < 0.0001

UF Trips 7-12 Color 23.68 < 0.0001

Chl_a 29.36 < 0.0001

WQMN 1996-1998 TSS 89.55 < 0.0001

Color 69.47 < 0.0001

WQMN 1999 TSS 3.02 0.0938
Chl_a 1.47 0.2357

Phlips TSS 2.29 0.1499
Color 0.85 0.3715

SERC Color 132.64 < 0.0001
Chl_a 10.49 0.0021

0.4411) (Table 3.6). With three variables, the models for the combined data set, HBOI

Year 1, UF Trips 1-6, WQMN 1996-1998, and SERC all have R2 values indicating real world

significance with SERC again having the highest R2 value with R2 = 0.7618.

Since the third variable is prescribed and not chosen from a pool of variables to give

the best fit for the model, the third variable in many of the data sets ends up being

statistically insignificant at the 0.05 level. This, as shown in Table 3.7, is the case for both

UF data sets. All three of the variables for WQMN 1999 and Phlips showed no statistical

significance at the 0.05 level.

Table 3.5: Best three-variable regression model for each data set.

Data Coefficient for Coefficient for Coefficient for Intercept
Set TSS Color Chl_a

All Sets 0.03275 0.01774 0.02373 0.18468

HBOI Year 1 0.07300 0.03110 0.00639 -0.57740

HBOI Year 2 0.02774 0.02176 0.02656 0.18644

UF Trips 1-6 0.05400 -0.00831 0.04914 0.45681

UF Trips 7-12 0.01064 0.01268 0.03810 0.26555

WQMN 1996-1998 0.02544 0.01458 0.00932 0.33958

WQMN 1999 0.02163 0.00281 0.04136 0.45431

Phlips 0.04421 0.03498 -0.00463 0.29913

SERC 0.01675 0.01632 0.01377 0.57898

Table 3.6: R2 values for the best three-variable model for each data
set and the improvement in R2 over the two- variable model.

Data Set R2 R2 Improvement

All Sets 0.3674 0.0539

HBOI Year 1 0.3851 0.0029

HBOI Year 2 0.2849 0.0390

UF Trips 1-6 0.4411 0.0017

UF Trips 7-12 0.2904 0.0151

WQMN 1996-1998 0.3703 0.0111

WQMN 1999 0.1160 0.0016

Phlips 0.1310 0.0013

SERC 0.7618 0.0243

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